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authorGravatar Samuel Mimram <smimram@debian.org>2008-07-25 15:12:53 +0200
committerGravatar Samuel Mimram <smimram@debian.org>2008-07-25 15:12:53 +0200
commita0cfa4f118023d35b767a999d5a2ac4b082857b4 (patch)
treedabcac548e299fee1da464c93b3dba98484f45b1 /test-suite
parent2281410e38ef99d025ea77194585a9bc019fdaa9 (diff)
Imported Upstream version 8.2~beta3+dfsgupstream/8.2.beta3+dfsg
Diffstat (limited to 'test-suite')
-rw-r--r--test-suite/bugs/closed/1519.v23
-rw-r--r--test-suite/bugs/closed/1780.v12
-rw-r--r--test-suite/bugs/closed/1787.v11
-rw-r--r--test-suite/bugs/closed/shouldfail/1703.v7
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1041.v13
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1100.v12
-rw-r--r--test-suite/bugs/closed/shouldsucceed/121.v17
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1243.v12
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1302.v22
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1322.v24
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1411.v35
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1414.v41
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1419.v8
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1425.v19
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1446.v20
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1448.v28
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1477.v18
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1483.v10
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1507.v121
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1519.v14
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1568.v13
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1576.v38
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1582.v15
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1604.v7
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1614.v21
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1618.v23
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1634.v24
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1643.v21
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1680.v9
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1683.v42
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1696.v16
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1704.v17
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1718.v9
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1738.v30
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1740.v23
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1754.v24
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1773.v9
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1774.v18
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1775.v39
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1776.v22
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1779.v25
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1784.v101
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1844.v217
-rw-r--r--test-suite/bugs/closed/shouldsucceed/1865.v18
-rw-r--r--test-suite/bugs/closed/shouldsucceed/348.v13
-rw-r--r--test-suite/bugs/closed/shouldsucceed/38.v22
-rw-r--r--test-suite/bugs/closed/shouldsucceed/545.v5
-rw-r--r--test-suite/bugs/closed/shouldsucceed/846.v213
-rw-r--r--test-suite/bugs/closed/shouldsucceed/931.v7
-rw-r--r--test-suite/bugs/opened/1773.v10
-rw-r--r--test-suite/bugs/opened/shouldnotfail/1338.v-disabled12
-rw-r--r--test-suite/bugs/opened/shouldnotfail/1416.v27
-rw-r--r--test-suite/bugs/opened/shouldnotfail/1501.v93
-rw-r--r--test-suite/bugs/opened/shouldnotfail/1596.v242
-rw-r--r--test-suite/bugs/opened/shouldnotfail/1811.v9
-rw-r--r--test-suite/bugs/opened/shouldnotfail/743.v12
-rwxr-xr-xtest-suite/check98
-rw-r--r--test-suite/complexity/injection.v113
-rw-r--r--test-suite/complexity/ring.v7
-rw-r--r--test-suite/complexity/ring2.v51
-rw-r--r--test-suite/csdp.cache106548
-rw-r--r--test-suite/failure/circular_subtyping1.v7
-rw-r--r--test-suite/failure/circular_subtyping2.v8
-rw-r--r--test-suite/failure/fixpoint2.v6
-rw-r--r--test-suite/failure/guard.v10
-rw-r--r--test-suite/failure/rewrite_in_hyp2.v8
-rw-r--r--test-suite/failure/subtyping.v21
-rw-r--r--test-suite/failure/subtyping2.v245
-rw-r--r--test-suite/failure/univ_include.v30
-rw-r--r--test-suite/ide/undo.v79
-rw-r--r--test-suite/ideal-features/Case9.v12
-rw-r--r--test-suite/ideal-features/complexity/evars_subst.v53
-rw-r--r--test-suite/ideal-features/evars_subst.v53
-rw-r--r--test-suite/ideal-features/universes.v43
-rw-r--r--test-suite/micromega/bertot.v22
-rw-r--r--test-suite/micromega/example.v347
-rw-r--r--test-suite/micromega/heap3_vcgen_25.v38
-rw-r--r--test-suite/micromega/qexample.v62
-rw-r--r--test-suite/micromega/rexample.v62
-rw-r--r--test-suite/micromega/square.v61
-rw-r--r--test-suite/micromega/zomicron.v27
-rw-r--r--test-suite/modules/pseudo_circular_with.v6
-rw-r--r--test-suite/modules/resolver.v37
-rw-r--r--test-suite/modules/subtyping.v46
-rw-r--r--test-suite/output/Cases.out21
-rw-r--r--test-suite/output/Cases.v29
-rw-r--r--test-suite/output/Fixpoint.out14
-rw-r--r--test-suite/output/Fixpoint.v23
-rw-r--r--test-suite/output/Implicit.out5
-rw-r--r--test-suite/output/Implicit.v19
-rw-r--r--test-suite/output/InitSyntax.out3
-rw-r--r--test-suite/output/Nametab.out36
-rw-r--r--test-suite/output/Nametab.v22
-rw-r--r--test-suite/output/Notations.out4
-rw-r--r--test-suite/output/Notations.v10
-rw-r--r--test-suite/output/Tactics.out2
-rw-r--r--test-suite/output/TranspModtype.out3
-rw-r--r--test-suite/output/ZSyntax.out10
-rw-r--r--test-suite/output/reduction.out4
-rw-r--r--test-suite/output/reduction.v13
-rw-r--r--test-suite/success/AdvancedCanonicalStructure.v144
-rw-r--r--test-suite/success/Case18.v12
-rw-r--r--test-suite/success/Cases-bug1834.v13
-rw-r--r--test-suite/success/Cases.v5
-rw-r--r--test-suite/success/CasesDep.v58
-rw-r--r--test-suite/success/Discriminate.v23
-rw-r--r--test-suite/success/Fixpoint.v19
-rw-r--r--test-suite/success/ImplicitArguments.v17
-rw-r--r--test-suite/success/Injection.v27
-rw-r--r--test-suite/success/LetPat.v55
-rw-r--r--test-suite/success/Notations.v16
-rw-r--r--test-suite/success/Omega.v14
-rw-r--r--test-suite/success/OmegaPre.v127
-rw-r--r--test-suite/success/ROmega.v20
-rw-r--r--test-suite/success/ROmegaPre.v127
-rw-r--r--test-suite/success/apply.v193
-rw-r--r--test-suite/success/cc.v9
-rw-r--r--test-suite/success/change.v6
-rw-r--r--test-suite/success/clear.v13
-rw-r--r--test-suite/success/conv_pbs.v223
-rw-r--r--test-suite/success/decl_mode.v182
-rw-r--r--test-suite/success/dependentind.v100
-rw-r--r--test-suite/success/destruct.v32
-rw-r--r--test-suite/success/evars.v136
-rw-r--r--test-suite/success/extraction.v2
-rw-r--r--test-suite/success/fix.v59
-rw-r--r--test-suite/success/hyps_inclusion.v32
-rw-r--r--test-suite/success/implicit.v10
-rw-r--r--test-suite/success/ltac.v47
-rw-r--r--test-suite/success/options.v2
-rw-r--r--test-suite/success/parsing.v8
-rw-r--r--test-suite/success/pattern.v7
-rw-r--r--test-suite/success/refine.v30
-rw-r--r--test-suite/success/rewrite.v21
-rw-r--r--test-suite/success/setoid_test.v14
-rw-r--r--test-suite/success/setoid_test2.v4
-rw-r--r--test-suite/success/setoid_test_function_space.v12
-rw-r--r--test-suite/success/specialize.v48
-rw-r--r--test-suite/success/unification.v65
-rw-r--r--test-suite/success/univers.v4
-rw-r--r--test-suite/typeclasses/NewSetoid.v74
-rw-r--r--test-suite/typeclasses/clrewrite.v111
-rw-r--r--test-suite/typeclasses/unification_delta.v46
143 files changed, 112307 insertions, 91 deletions
diff --git a/test-suite/bugs/closed/1519.v b/test-suite/bugs/closed/1519.v
new file mode 100644
index 00000000..98e3e214
--- /dev/null
+++ b/test-suite/bugs/closed/1519.v
@@ -0,0 +1,23 @@
+Section S.
+
+ Variable A:Prop.
+ Variable W:A.
+
+ Remark T: A -> A.
+ intro Z.
+ rename W into Z_.
+ rename Z into W.
+ rename Z_ into Z.
+ exact Z.
+ Qed.
+
+ (* bug :
+ Error:
+ Unbound reference: In environment
+ A : Prop
+ W : A
+ Z : A
+ The reference 2 is free
+ *)
+
+End S.
diff --git a/test-suite/bugs/closed/1780.v b/test-suite/bugs/closed/1780.v
new file mode 100644
index 00000000..3929fbae
--- /dev/null
+++ b/test-suite/bugs/closed/1780.v
@@ -0,0 +1,12 @@
+
+Definition bug := Eval vm_compute in eq_rect.
+(* bug:
+Error: Illegal application (Type Error):
+The term "eq" of type "forall A : Type, A -> A -> Prop"
+cannot be applied to the terms
+ "x" : "A"
+ "P" : "A -> Type"
+ "x0" : "A"
+The 1st term has type "A" which should be coercible to
+"Type".
+*)
diff --git a/test-suite/bugs/closed/1787.v b/test-suite/bugs/closed/1787.v
new file mode 100644
index 00000000..8e1024e6
--- /dev/null
+++ b/test-suite/bugs/closed/1787.v
@@ -0,0 +1,11 @@
+Parameter P : nat -> nat -> Prop.
+Parameter Q : nat -> nat -> Prop.
+Axiom A : forall x x' x'', P x x' -> Q x'' x' -> P x x''.
+
+Goal (P 1 3) -> (Q 1 3) -> (P 1 1).
+intros H H'.
+refine ((fun H1 : P 1 _ => let H2 := (_:Q 1 _) in A _ _ _ H1 H2) _).
+clear.
+Admitted.
+
+
diff --git a/test-suite/bugs/closed/shouldfail/1703.v b/test-suite/bugs/closed/shouldfail/1703.v
new file mode 100644
index 00000000..6b5198cc
--- /dev/null
+++ b/test-suite/bugs/closed/shouldfail/1703.v
@@ -0,0 +1,7 @@
+(* Check correct binding of intros until used in Ltac *)
+
+Ltac intros_until n := intros until n.
+
+Goal forall i j m n : nat, i = 0 /\ j = 0 /\ m = 0 /\ n = 0.
+intro i.
+intros until i.
diff --git a/test-suite/bugs/closed/shouldsucceed/1041.v b/test-suite/bugs/closed/shouldsucceed/1041.v
new file mode 100644
index 00000000..a5de82e0
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1041.v
@@ -0,0 +1,13 @@
+Goal Prop.
+
+pose (P:=(fun x y :Prop => y)).
+evar (Q: (forall X Y,P X Y -> Prop)) .
+
+instantiate (1:= fun _ => _ ) in (Value of Q).
+instantiate (1:= fun _ => _ ) in (Value of Q).
+instantiate (1:= fun _ => _ ) in (Value of Q).
+
+instantiate (1:=H) in (Value of Q).
+
+Admitted.
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1100.v b/test-suite/bugs/closed/shouldsucceed/1100.v
new file mode 100644
index 00000000..6d619c74
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1100.v
@@ -0,0 +1,12 @@
+Require Import Setoid.
+
+Parameter P : nat -> Prop.
+Parameter Q : nat -> Prop.
+Parameter PQ : forall n, P n <-> Q n.
+
+Lemma PQ2 : forall n, P n -> Q n.
+ intros.
+ rewrite PQ in H.
+ trivial.
+Qed.
+
diff --git a/test-suite/bugs/closed/shouldsucceed/121.v b/test-suite/bugs/closed/shouldsucceed/121.v
new file mode 100644
index 00000000..d193aa73
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/121.v
@@ -0,0 +1,17 @@
+Require Import Setoid.
+
+Section Setoid_Bug.
+
+Variable X:Type -> Type.
+Variable Xeq : forall A, (X A) -> (X A) -> Prop.
+Hypothesis Xst : forall A, Equivalence (X A) (Xeq A).
+
+Variable map : forall A B, (A -> B) -> X A -> X B.
+
+Implicit Arguments map [A B].
+
+Goal forall A B (a b:X (B -> A)) (c:X A) (f:A -> B -> A), Xeq _ a b -> Xeq _ b (map f c) -> Xeq _ a (map f c).
+intros A B a b c f Hab Hbc.
+rewrite Hab.
+assumption.
+Qed.
diff --git a/test-suite/bugs/closed/shouldsucceed/1243.v b/test-suite/bugs/closed/shouldsucceed/1243.v
new file mode 100644
index 00000000..7d6781db
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1243.v
@@ -0,0 +1,12 @@
+Require Import ZArith.
+Require Import Arith.
+Open Scope Z_scope.
+
+Theorem r_ex : (forall x y:nat, x + y = x + y)%nat.
+Admitted.
+
+Theorem r_ex' : forall x y:nat, (x + y = x + y)%nat.
+Admitted.
+
+
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1302.v b/test-suite/bugs/closed/shouldsucceed/1302.v
new file mode 100644
index 00000000..e94dfcfb
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1302.v
@@ -0,0 +1,22 @@
+Module Type T.
+
+Parameter A : Type.
+
+Inductive L : Type :=
+| L0 : L (* without this constructor, it works right *)
+| L1 : A -> L.
+
+End T.
+
+Axiom Tp : Type.
+
+Module TT : T.
+
+Definition A : Type := Tp.
+
+Inductive L : Type :=
+| L0 : L
+| L1 : A -> L.
+
+End TT.
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1322.v b/test-suite/bugs/closed/shouldsucceed/1322.v
new file mode 100644
index 00000000..7e21aa7c
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1322.v
@@ -0,0 +1,24 @@
+Require Import Setoid.
+
+Section transition_gen.
+
+Variable I : Type.
+Variable I_eq :I -> I -> Prop.
+Variable I_eq_equiv : Setoid_Theory I I_eq.
+
+(* Add Relation I I_eq
+ reflexivity proved by I_eq_equiv.(Seq_refl I I_eq)
+ symmetry proved by I_eq_equiv.(Seq_sym I I_eq)
+ transitivity proved by I_eq_equiv.(Seq_trans I I_eq)
+as I_eq_relation. *)
+
+Add Setoid I I_eq I_eq_equiv as I_with_eq.
+
+Variable F : I -> Type.
+Variable F_morphism : forall i j, I_eq i j -> F i = F j.
+
+
+Add Morphism F with signature I_eq ==> (@eq _) as F_morphism2.
+Admitted.
+
+End transition_gen.
diff --git a/test-suite/bugs/closed/shouldsucceed/1411.v b/test-suite/bugs/closed/shouldsucceed/1411.v
new file mode 100644
index 00000000..e330d46f
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1411.v
@@ -0,0 +1,35 @@
+Require Import List.
+Require Import Program.
+
+Inductive Tree : Set :=
+| Br : Tree -> Tree -> Tree
+| No : nat -> Tree
+.
+
+(* given a tree, we want to know which lists can
+ be used to navigate exactly to a node *)
+Inductive Exact : Tree -> list bool -> Prop :=
+| exDone n : Exact (No n) nil
+| exLeft l r p: Exact l p -> Exact (Br l r) (true::p)
+| exRight l r p: Exact r p -> Exact (Br l r) (false::p)
+.
+
+Definition unreachable A : False -> A.
+intros.
+destruct H.
+Defined.
+
+Program Fixpoint fetch t p (x:Exact t p) {struct t} :=
+ match t, p with
+ | No p' , nil => p'
+ | No p' , _::_ => unreachable nat _
+ | Br l r, nil => unreachable nat _
+ | Br l r, true::t => fetch l t _
+ | Br l r, false::t => fetch r t _
+ end.
+
+Next Obligation. inversion x. Qed.
+Next Obligation. inversion x. Qed.
+Next Obligation. inversion x; trivial. Qed.
+Next Obligation. inversion x; trivial. Qed.
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1414.v b/test-suite/bugs/closed/shouldsucceed/1414.v
new file mode 100644
index 00000000..d3c00808
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1414.v
@@ -0,0 +1,41 @@
+Require Import ZArith Coq.Program.Wf Coq.Program.Utils.
+
+Parameter data:Set.
+
+Inductive t : Set :=
+ | Leaf : t
+ | Node : t -> data -> t -> Z -> t.
+
+Parameter avl : t -> Prop.
+Parameter bst : t -> Prop.
+Parameter In : data -> t -> Prop.
+Parameter cardinal : t -> nat.
+Definition card2 (s:t*t) := let (s1,s2) := s in cardinal s1 + cardinal s2.
+
+Parameter split : data -> t -> t*(bool*t).
+Parameter join : t -> data -> t -> t.
+Parameter add : data -> t -> t.
+
+Program Fixpoint union
+ (s:t*t)
+ (hb1: bst (fst s))(ha1: avl (fst s))(hb2: bst (snd s))(hb2: avl (snd s))
+ { measure card2 s } :
+ {s' : t | bst s' /\ avl s' /\ forall x, In x s' <-> In x (fst s) \/ In x (snd
+s)} :=
+ match s with
+ | (Leaf,t2) => t2
+ | (t1,Leaf) => t1
+ | (Node l1 v1 r1 h1, Node l2 v2 r2 h2) =>
+ if (Z_ge_lt_dec h1 h2) then
+ if (Z_eq_dec h2 1)
+ then add v2 (fst s)
+ else
+ let (l2', r2') := split v1 (snd s) in
+ join (union (l1,l2') _ _ _ _) v1 (union (r1,snd r2') _ _ _ _)
+ else
+ if (Z_eq_dec h1 1)
+ then add v1 (snd s)
+ else
+ let (l1', r1') := split v2 (fst s) in
+ join (union (l1',l2) _ _ _ _) v2 (union (snd r1',r2) _ _ _ _)
+ end.
diff --git a/test-suite/bugs/closed/shouldsucceed/1419.v b/test-suite/bugs/closed/shouldsucceed/1419.v
new file mode 100644
index 00000000..d021107d
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1419.v
@@ -0,0 +1,8 @@
+Goal True.
+ set(a := 0).
+ set(b := a).
+ unfold a in b.
+ clear a.
+ Eval vm_compute in b.
+ trivial.
+Qed.
diff --git a/test-suite/bugs/closed/shouldsucceed/1425.v b/test-suite/bugs/closed/shouldsucceed/1425.v
new file mode 100644
index 00000000..8e26209a
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1425.v
@@ -0,0 +1,19 @@
+Require Import Setoid.
+
+Parameter recursion : forall A : Set, A -> (nat -> A -> A) -> nat -> A.
+
+Axiom recursion_S :
+ forall (A : Set) (EA : relation A) (a : A) (f : nat -> A -> A) (n : nat),
+ EA (recursion A a f (S n)) (f n (recursion A a f n)).
+
+Goal forall n : nat, recursion nat 0 (fun _ _ => 1) (S n) = 1.
+intro n.
+rewrite recursion_S.
+reflexivity.
+Qed.
+
+Goal forall n : nat, recursion nat 0 (fun _ _ => 1) (S n) = 1.
+intro n.
+setoid_rewrite recursion_S.
+reflexivity.
+Qed. \ No newline at end of file
diff --git a/test-suite/bugs/closed/shouldsucceed/1446.v b/test-suite/bugs/closed/shouldsucceed/1446.v
new file mode 100644
index 00000000..d4e7cea8
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1446.v
@@ -0,0 +1,20 @@
+Lemma not_true_eq_false : forall (b:bool), b <> true -> b = false.
+Proof.
+ destruct b;intros;trivial.
+ elim H.
+ exact (refl_equal true).
+Qed.
+
+Section BUG.
+
+ Variable b : bool.
+ Hypothesis H : b <> true.
+ Hypothesis H0 : b = true.
+ Hypothesis H1 : b <> true.
+
+ Goal False.
+ rewrite (not_true_eq_false _ H) in * |-.
+ contradiction.
+ Qed.
+
+End BUG.
diff --git a/test-suite/bugs/closed/shouldsucceed/1448.v b/test-suite/bugs/closed/shouldsucceed/1448.v
new file mode 100644
index 00000000..fe3b4c8b
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1448.v
@@ -0,0 +1,28 @@
+Require Import Relations.
+Require Import Setoid.
+Require Import Ring_theory.
+Require Import Ring_base.
+
+
+Variable R : Type.
+Variable Rone Rzero : R.
+Variable Rplus Rmult Rminus : R -> R -> R.
+Variable Rneg : R -> R.
+
+Lemma my_ring_theory : @ring_theory R Rzero Rone Rplus Rmult Rminus Rneg (@eq
+R).
+Admitted.
+
+Variable Req : R -> R -> Prop.
+
+Hypothesis Req_refl : reflexive _ Req.
+Hypothesis Req_sym : symmetric _ Req.
+Hypothesis Req_trans : transitive _ Req.
+
+Add Relation R Req
+ reflexivity proved by Req_refl
+ symmetry proved by Req_sym
+ transitivity proved by Req_trans
+ as Req_rel.
+
+Add Ring my_ring : my_ring_theory (abstract).
diff --git a/test-suite/bugs/closed/shouldsucceed/1477.v b/test-suite/bugs/closed/shouldsucceed/1477.v
new file mode 100644
index 00000000..dfc8c328
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1477.v
@@ -0,0 +1,18 @@
+Inductive I : Set :=
+ | A : nat -> nat -> I
+ | B : nat -> nat -> I.
+
+Definition foo1 (x:I) : nat :=
+ match x with
+ | A a b | B a b => S b
+ end.
+
+Definition foo2 (x:I) : nat :=
+ match x with
+ | A _ b | B b _ => S b
+ end.
+
+Definition foo (x:I) : nat :=
+ match x with
+ | A a b | B b a => S b
+ end.
diff --git a/test-suite/bugs/closed/shouldsucceed/1483.v b/test-suite/bugs/closed/shouldsucceed/1483.v
new file mode 100644
index 00000000..a3d7f168
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1483.v
@@ -0,0 +1,10 @@
+Require Import BinPos.
+
+Definition P := (fun x : positive => x = xH).
+
+Goal forall (p q : positive), P q -> q = p -> P p.
+intros; congruence.
+Qed.
+
+
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1507.v b/test-suite/bugs/closed/shouldsucceed/1507.v
new file mode 100644
index 00000000..b484c7dc
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1507.v
@@ -0,0 +1,121 @@
+(*
+ Implementing reals a la Stolzenberg
+
+ Danko Ilik, March 2007
+ svn revision: $Id: 1507.v 10068 2007-08-10 12:06:59Z notin $
+
+ XField.v -- (unfinished) axiomatisation of the theories of real and
+ rational intervals.
+*)
+
+Definition associative (A:Type)(op:A->A->A) :=
+ forall x y z:A, op (op x y) z = op x (op y z).
+
+Definition commutative (A:Type)(op:A->A->A) :=
+ forall x y:A, op x y = op y x.
+
+Definition trichotomous (A:Type)(R:A->A->Prop) :=
+ forall x y:A, R x y \/ x=y \/ R y x.
+
+Definition relation (A:Type) := A -> A -> Prop.
+Definition reflexive (A:Type)(R:relation A) := forall x:A, R x x.
+Definition transitive (A:Type)(R:relation A) :=
+ forall x y z:A, R x y -> R y z -> R x z.
+Definition symmetric (A:Type)(R:relation A) := forall x y:A, R x y -> R y x.
+
+Record interval (X:Set)(le:X->X->Prop) : Set :=
+ interval_make {
+ interval_left : X;
+ interval_right : X;
+ interval_nonempty : le interval_left interval_right
+ }.
+
+Record I (grnd:Set)(le:grnd->grnd->Prop) : Type := Imake {
+ Icar := interval grnd le;
+ Iplus : Icar -> Icar -> Icar;
+ Imult : Icar -> Icar -> Icar;
+ Izero : Icar;
+ Ione : Icar;
+ Iopp : Icar -> Icar;
+ Iinv : Icar -> Icar;
+ Ic : Icar -> Icar -> Prop; (* consistency *)
+ (* monoids *)
+ Iplus_assoc : associative Icar Iplus;
+ Imult_assoc : associative Icar Imult;
+ (* abelian groups *)
+ Iplus_comm : commutative Icar Iplus;
+ Imult_comm : commutative Icar Imult;
+ Iplus_0_l : forall x:Icar, Ic (Iplus Izero x) x;
+ Iplus_0_r : forall x:Icar, Ic (Iplus x Izero) x;
+ Imult_0_l : forall x:Icar, Ic (Imult Ione x) x;
+ Imult_0_r : forall x:Icar, Ic (Imult x Ione) x;
+ Iplus_opp_r : forall x:Icar, Ic (Iplus x (Iopp x)) (Izero);
+ Imult_inv_r : forall x:Icar, ~(Ic x Izero) -> Ic (Imult x (Iinv x)) Ione;
+ (* distributive laws *)
+ Imult_plus_distr_l : forall x x' y y' z z' z'',
+ Ic x x' -> Ic y y' -> Ic z z' -> Ic z z'' ->
+ Ic (Imult (Iplus x y) z) (Iplus (Imult x' z') (Imult y' z''));
+ (* order and lattice structure *)
+ Ilt : Icar -> Icar -> Prop;
+ Ilc := fun (x y:Icar) => Ilt x y \/ Ic x y;
+ Isup : Icar -> Icar -> Icar;
+ Iinf : Icar -> Icar -> Icar;
+ Ilt_trans : transitive _ lt;
+ Ilt_trich : forall x y:Icar, Ilt x y \/ Ic x y \/ Ilt y x;
+ Isup_lub : forall x y z:Icar, Ilc x z -> Ilc y z -> Ilc (Isup x y) z;
+ Iinf_glb : forall x y z:Icar, Ilc x y -> Ilc x z -> Ilc x (Iinf y z);
+ (* order preserves operations? *)
+ (* properties of Ic *)
+ Ic_refl : reflexive _ Ic;
+ Ic_sym : symmetric _ Ic
+}.
+
+Definition interval_set (X:Set)(le:X->X->Prop) :=
+ (interval X le) -> Prop. (* can be Set as well *)
+Check interval_set.
+Check Ic.
+Definition consistent (X:Set)(le:X->X->Prop)(TI:I X le)(p:interval_set X le) :=
+ forall I J:interval X le, p I -> p J -> (Ic X le TI) I J.
+Check consistent.
+(* define 'fine' *)
+
+Record N (grnd:Set)(le:grnd->grnd->Prop)(grndI:I grnd le) : Type := Nmake {
+ Ncar := interval_set grnd le;
+ Nplus : Ncar -> Ncar -> Ncar;
+ Nmult : Ncar -> Ncar -> Ncar;
+ Nzero : Ncar;
+ None : Ncar;
+ Nopp : Ncar -> Ncar;
+ Ninv : Ncar -> Ncar;
+ Nc : Ncar -> Ncar -> Prop; (* Ncistency *)
+ (* monoids *)
+ Nplus_assoc : associative Ncar Nplus;
+ Nmult_assoc : associative Ncar Nmult;
+ (* abelian groups *)
+ Nplus_comm : commutative Ncar Nplus;
+ Nmult_comm : commutative Ncar Nmult;
+ Nplus_0_l : forall x:Ncar, Nc (Nplus Nzero x) x;
+ Nplus_0_r : forall x:Ncar, Nc (Nplus x Nzero) x;
+ Nmult_0_l : forall x:Ncar, Nc (Nmult None x) x;
+ Nmult_0_r : forall x:Ncar, Nc (Nmult x None) x;
+ Nplus_opp_r : forall x:Ncar, Nc (Nplus x (Nopp x)) (Nzero);
+ Nmult_inv_r : forall x:Ncar, ~(Nc x Nzero) -> Nc (Nmult x (Ninv x)) None;
+ (* distributive laws *)
+ Nmult_plus_distr_l : forall x x' y y' z z' z'',
+ Nc x x' -> Nc y y' -> Nc z z' -> Nc z z'' ->
+ Nc (Nmult (Nplus x y) z) (Nplus (Nmult x' z') (Nmult y' z''));
+ (* order and lattice structure *)
+ Nlt : Ncar -> Ncar -> Prop;
+ Nlc := fun (x y:Ncar) => Nlt x y \/ Nc x y;
+ Nsup : Ncar -> Ncar -> Ncar;
+ Ninf : Ncar -> Ncar -> Ncar;
+ Nlt_trans : transitive _ lt;
+ Nlt_trich : forall x y:Ncar, Nlt x y \/ Nc x y \/ Nlt y x;
+ Nsup_lub : forall x y z:Ncar, Nlc x z -> Nlc y z -> Nlc (Nsup x y) z;
+ Ninf_glb : forall x y z:Ncar, Nlc x y -> Nlc x z -> Nlc x (Ninf y z);
+ (* order preserves operations? *)
+ (* properties of Nc *)
+ Nc_refl : reflexive _ Nc;
+ Nc_sym : symmetric _ Nc
+}.
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1519.v b/test-suite/bugs/closed/shouldsucceed/1519.v
new file mode 100644
index 00000000..66bab241
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1519.v
@@ -0,0 +1,14 @@
+Section S.
+
+ Variable A:Prop.
+ Variable W:A.
+
+ Remark T: A -> A.
+ intro Z.
+ rename W into Z_.
+ rename Z into W.
+ rename Z_ into Z.
+ exact Z.
+ Qed.
+
+End S.
diff --git a/test-suite/bugs/closed/shouldsucceed/1568.v b/test-suite/bugs/closed/shouldsucceed/1568.v
new file mode 100644
index 00000000..9f10f749
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1568.v
@@ -0,0 +1,13 @@
+CoInductive A: Set :=
+ mk_A: B -> A
+with B: Set :=
+ mk_B: A -> B.
+
+CoFixpoint a:A := mk_A b
+with b:B := mk_B a.
+
+Goal b = match a with mk_A a1 => a1 end.
+ simpl. reflexivity.
+Qed.
+
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1576.v b/test-suite/bugs/closed/shouldsucceed/1576.v
new file mode 100644
index 00000000..c9ebbd14
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1576.v
@@ -0,0 +1,38 @@
+Module Type TA.
+Parameter t : Set.
+End TA.
+
+Module Type TB.
+Declare Module A: TA.
+End TB.
+
+Module Type TC.
+Declare Module B : TB.
+End TC.
+
+Module Type TD.
+
+Declare Module B: TB .
+Declare Module C: TC
+ with Module B := B .
+End TD.
+
+Module Type TE.
+Declare Module D : TD.
+End TE.
+
+Module Type TF.
+Declare Module E: TE.
+End TF.
+
+Module G (D: TD).
+Module B' := D.C.B.
+End G.
+
+Module H (F: TF).
+Module I := G(F.E.D).
+End H.
+
+Declare Module F: TF.
+Module K := H(F).
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1582.v b/test-suite/bugs/closed/shouldsucceed/1582.v
new file mode 100644
index 00000000..47953a66
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1582.v
@@ -0,0 +1,15 @@
+Require Import Peano_dec.
+
+Definition fact_F :
+ forall (n:nat),
+ (forall m, m<n -> nat) ->
+ nat.
+refine
+ (fun n fact_rec =>
+ if eq_nat_dec n 0 then
+ 1
+ else
+ let fn := fact_rec (n-1) _ in
+ n * fn).
+Admitted.
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1604.v b/test-suite/bugs/closed/shouldsucceed/1604.v
new file mode 100644
index 00000000..22c3df82
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1604.v
@@ -0,0 +1,7 @@
+Require Import Setoid.
+
+Parameter F : nat -> nat.
+Axiom F_id : forall n : nat, n = F n.
+Goal forall n : nat, F n = n.
+intro n. setoid_rewrite F_id at 3. reflexivity.
+Qed.
diff --git a/test-suite/bugs/closed/shouldsucceed/1614.v b/test-suite/bugs/closed/shouldsucceed/1614.v
new file mode 100644
index 00000000..6bc165d4
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1614.v
@@ -0,0 +1,21 @@
+Require Import Ring.
+Require Import ArithRing.
+
+Fixpoint eq_nat_bool (x y : nat) {struct x} : bool :=
+match x, y with
+| 0, 0 => true
+| S x', S y' => eq_nat_bool x' y'
+| _, _ => false
+end.
+
+Theorem eq_nat_bool_implies_eq : forall x y, eq_nat_bool x y = true -> x = y.
+Proof.
+induction x; destruct y; simpl; intro H; try (reflexivity || inversion H).
+apply IHx in H; rewrite H; reflexivity.
+Qed.
+
+Add Ring MyNatSRing : natSRth (decidable eq_nat_bool_implies_eq).
+
+Goal 0 = 0.
+ ring.
+Qed.
diff --git a/test-suite/bugs/closed/shouldsucceed/1618.v b/test-suite/bugs/closed/shouldsucceed/1618.v
new file mode 100644
index 00000000..a90290bf
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1618.v
@@ -0,0 +1,23 @@
+Inductive A: Set :=
+| A1: nat -> A.
+
+Definition A_size (a: A) : nat :=
+ match a with
+ | A1 n => 0
+ end.
+
+Require Import Recdef.
+
+Function n3 (P: A -> Prop) (f: forall n, P (A1 n)) (a: A) {struct a} : P a :=
+ match a return (P a) with
+ | A1 n => f n
+ end.
+
+
+Function n1 (P: A -> Prop) (f: forall n, P (A1 n)) (a: A) {measure A_size a} :
+P
+a :=
+ match a return (P a) with
+ | A1 n => f n
+ end.
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1634.v b/test-suite/bugs/closed/shouldsucceed/1634.v
new file mode 100644
index 00000000..e0c540f3
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1634.v
@@ -0,0 +1,24 @@
+Require Export Relation_Definitions.
+Require Export Setoid.
+
+Variable A : Type.
+Variable S : A -> Type.
+Variable Seq : forall {a:A}, relation (S a).
+
+Hypothesis Seq_refl : forall {a:A} (x : S a), Seq x x.
+Hypothesis Seq_sym : forall {a:A} (x y : S a), Seq x y -> Seq y x.
+Hypothesis Seq_trans : forall {a:A} (x y z : S a), Seq x y -> Seq y z ->
+Seq x z.
+
+Add Parametric Relation a : (S a) Seq
+ reflexivity proved by Seq_refl
+ symmetry proved by Seq_sym
+ transitivity proved by Seq_trans
+ as S_Setoid.
+
+Goal forall (a : A) (x y : S a), Seq x y -> Seq x y.
+ intros a x y H.
+ setoid_replace x with y.
+ reflexivity.
+ trivial.
+Qed.
diff --git a/test-suite/bugs/closed/shouldsucceed/1643.v b/test-suite/bugs/closed/shouldsucceed/1643.v
new file mode 100644
index 00000000..4114987d
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1643.v
@@ -0,0 +1,21 @@
+(* Check some aspects of that the algorithm used to possibly reuse a
+ global name in the recursive calls (coinductive case) *)
+
+CoInductive Str : Set := Cons (h:nat) (t:Str).
+
+Definition decomp_func (s:Str) :=
+ match s with
+ | Cons h t => Cons h t
+ end.
+
+Theorem decomp s: s = decomp_func s.
+Proof.
+ intros s.
+ case s; simpl; reflexivity.
+Qed.
+
+Definition zeros := (cofix z : Str := Cons 0 z).
+Lemma zeros_rw : zeros = Cons 0 zeros.
+ rewrite (decomp zeros).
+ simpl.
+Admitted.
diff --git a/test-suite/bugs/closed/shouldsucceed/1680.v b/test-suite/bugs/closed/shouldsucceed/1680.v
new file mode 100644
index 00000000..524c7bab
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1680.v
@@ -0,0 +1,9 @@
+Ltac int1 := let h := fresh in intro h.
+
+Goal nat -> nat -> True.
+ let h' := fresh in (let h := fresh in intro h); intro h'.
+ Restart. let h' := fresh in int1; intro h'.
+ trivial.
+Qed.
+
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1683.v b/test-suite/bugs/closed/shouldsucceed/1683.v
new file mode 100644
index 00000000..1571ee20
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1683.v
@@ -0,0 +1,42 @@
+Require Import Setoid.
+
+Section SetoidBug.
+
+Variable ms : Type.
+Variable ms_type : ms -> Type.
+Variable ms_eq : forall (A:ms), relation (ms_type A).
+
+Variable CR : ms.
+
+Record Ring : Type :=
+{Ring_type : Type}.
+
+Variable foo : forall (A:Ring), nat -> Ring_type A.
+Variable IR : Ring.
+Variable IRasCR : Ring_type IR -> ms_type CR.
+
+Definition CRasCRing : Ring := Build_Ring (ms_type CR).
+
+Hypothesis ms_refl : forall A x, ms_eq A x x.
+Hypothesis ms_sym : forall A x y, ms_eq A x y -> ms_eq A y x.
+Hypothesis ms_trans : forall A x y z, ms_eq A x y -> ms_eq A y z -> ms_eq A x z.
+
+Add Parametric Relation A : (ms_type A) (ms_eq A)
+ reflexivity proved by (ms_refl A)
+ symmetry proved by (ms_sym A)
+ transitivity proved by (ms_trans A)
+ as ms_Setoid.
+
+Hypothesis foobar : forall n, ms_eq CR (IRasCR (foo IR n)) (foo CRasCRing n).
+
+Goal forall (b:ms_type CR),
+ ms_eq CR (IRasCR (foo IR O)) b ->
+ ms_eq CR (IRasCR (foo IR O)) b.
+intros b H.
+rewrite foobar.
+rewrite foobar in H.
+assumption.
+Qed.
+
+
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1696.v b/test-suite/bugs/closed/shouldsucceed/1696.v
new file mode 100644
index 00000000..0826428a
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1696.v
@@ -0,0 +1,16 @@
+Require Import Setoid.
+
+Inductive mynat := z : mynat | s : mynat -> mynat.
+
+Parameter E : mynat -> mynat -> Prop.
+Axiom E_equiv : equiv mynat E.
+
+Add Relation mynat E
+ reflexivity proved by (proj1 E_equiv)
+ symmetry proved by (proj2 (proj2 E_equiv))
+ transitivity proved by (proj1 (proj2 E_equiv))
+as E_rel.
+
+Notation "x == y" := (E x y) (at level 70).
+
+Goal z == s z -> s z == z. intros H. setoid_rewrite H at 2. reflexivity. Qed.
diff --git a/test-suite/bugs/closed/shouldsucceed/1704.v b/test-suite/bugs/closed/shouldsucceed/1704.v
new file mode 100644
index 00000000..4b02d5f9
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1704.v
@@ -0,0 +1,17 @@
+
+Require Import Setoid.
+Parameter E : nat -> nat -> Prop.
+Axiom E_equiv : equiv nat E.
+Add Relation nat E
+reflexivity proved by (proj1 E_equiv)
+symmetry proved by (proj2 (proj2 E_equiv))
+transitivity proved by (proj1 (proj2 E_equiv))
+as E_rel.
+Notation "x == y" := (E x y) (at level 70, no associativity).
+Axiom r : False -> 0 == 1.
+Goal 0 == 0.
+Proof.
+rewrite r.
+reflexivity.
+admit.
+Qed.
diff --git a/test-suite/bugs/closed/shouldsucceed/1718.v b/test-suite/bugs/closed/shouldsucceed/1718.v
new file mode 100644
index 00000000..715fa941
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1718.v
@@ -0,0 +1,9 @@
+(* lazy delta unfolding used to miss delta on rels and vars (fixed in 10172) *)
+
+Check
+ let g := fun _ => 0 in
+ fix f (n : nat) :=
+ match n with
+ | 0 => g f
+ | S n' => 0
+ end.
diff --git a/test-suite/bugs/closed/shouldsucceed/1738.v b/test-suite/bugs/closed/shouldsucceed/1738.v
new file mode 100644
index 00000000..0deed366
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1738.v
@@ -0,0 +1,30 @@
+Require Import FSets.
+
+Module SomeSetoids (Import M:FSetInterface.S).
+
+Lemma Equal_refl : forall s, s[=]s.
+Proof. red; split; auto. Qed.
+
+Add Relation t Equal
+ reflexivity proved by Equal_refl
+ symmetry proved by eq_sym
+ transitivity proved by eq_trans
+ as EqualSetoid.
+
+Add Morphism Empty with signature Equal ==> iff as Empty_m.
+Proof.
+unfold Equal, Empty; firstorder.
+Qed.
+
+End SomeSetoids.
+
+Module Test (Import M:FSetInterface.S).
+ Module A:=SomeSetoids M.
+ Module B:=SomeSetoids M. (* lots of warning *)
+
+ Lemma Test : forall s s', s[=]s' -> Empty s -> Empty s'.
+ intros.
+ rewrite H in H0.
+ assumption.
+Qed.
+End Test. \ No newline at end of file
diff --git a/test-suite/bugs/closed/shouldsucceed/1740.v b/test-suite/bugs/closed/shouldsucceed/1740.v
new file mode 100644
index 00000000..d9ce546a
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1740.v
@@ -0,0 +1,23 @@
+(* Check that expansion of alias in pattern-matching compilation is no
+ longer dependent of whether the pattern-matching problem occurs in a
+ typed context or at toplevel (solved from revision 10883) *)
+
+Definition f :=
+ fun n m : nat =>
+ match n, m with
+ | O, _ => O
+ | n, O => n
+ | _, _ => O
+ end.
+
+Goal f =
+ fun n m : nat =>
+ match n, m with
+ | O, _ => O
+ | n, O => n
+ | _, _ => O
+ end.
+ unfold f.
+ reflexivity.
+Qed.
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1754.v b/test-suite/bugs/closed/shouldsucceed/1754.v
new file mode 100644
index 00000000..06b8dce8
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1754.v
@@ -0,0 +1,24 @@
+Axiom hp : Set.
+Axiom cont : nat -> hp -> Prop.
+Axiom sconj : (hp -> Prop) -> (hp -> Prop) -> hp -> Prop.
+Axiom sconjImpl : forall h A B,
+ (sconj A B) h -> forall (A' B': hp -> Prop),
+ (forall h', A h' -> A' h') ->
+ (forall h', B h' -> B' h') ->
+ (sconj A' B') h.
+
+Definition cont' (h:hp) := exists y, cont y h.
+
+Lemma foo : forall h x y A,
+ (sconj (cont x) (sconj (cont y) A)) h ->
+ (sconj cont' (sconj cont' A)) h.
+Proof.
+ intros h x y A H.
+ eapply sconjImpl.
+ 2:intros h' Hp'; econstructor; apply Hp'.
+ 2:intros h' Hp'; eapply sconjImpl.
+ 3:intros h'' Hp''; econstructor; apply Hp''.
+ 3:intros h'' Hp''; apply Hp''.
+ 2:apply Hp'.
+ clear H.
+Admitted.
diff --git a/test-suite/bugs/closed/shouldsucceed/1773.v b/test-suite/bugs/closed/shouldsucceed/1773.v
new file mode 100644
index 00000000..211af89b
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1773.v
@@ -0,0 +1,9 @@
+(* An occur-check test was done too early *)
+
+Goal forall B C : nat -> nat -> Prop, forall k,
+ (exists A, (forall k', C A k' -> B A k') -> B A k).
+Proof.
+ intros B C k.
+ econstructor.
+ intros X.
+ apply X. (* used to fail here *)
diff --git a/test-suite/bugs/closed/shouldsucceed/1774.v b/test-suite/bugs/closed/shouldsucceed/1774.v
new file mode 100644
index 00000000..4c24b481
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1774.v
@@ -0,0 +1,18 @@
+Axiom pl : (nat -> Prop) -> (nat -> Prop) -> (nat -> Prop).
+Axiom plImp : forall k P Q,
+ pl P Q k -> forall (P':nat -> Prop),
+ (forall k', P k' -> P' k') -> forall (Q':nat -> Prop),
+ (forall k', Q k' -> Q' k') ->
+ pl P' Q' k.
+
+Definition nexists (P:nat -> nat -> Prop) : nat -> Prop :=
+ fun k' => exists k, P k k'.
+
+Goal forall k (A:nat -> nat -> Prop) (B:nat -> Prop),
+ pl (nexists A) B k.
+intros.
+eapply plImp.
+2:intros m' M'; econstructor; apply M'.
+2:intros m' M'; apply M'.
+simpl.
+Admitted.
diff --git a/test-suite/bugs/closed/shouldsucceed/1775.v b/test-suite/bugs/closed/shouldsucceed/1775.v
new file mode 100644
index 00000000..dab4120b
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1775.v
@@ -0,0 +1,39 @@
+Axiom pair : nat -> nat -> nat -> Prop.
+Axiom pl : (nat -> Prop) -> (nat -> Prop) -> (nat -> Prop).
+Axiom plImp : forall k P Q,
+ pl P Q k -> forall (P':nat -> Prop),
+ (forall k', P k' -> P' k') -> forall (Q':nat -> Prop),
+ (forall k', Q k' -> Q' k') ->
+ pl P' Q' k.
+
+Definition nexists (P:nat -> nat -> Prop) : nat -> Prop :=
+ fun k' => exists k, P k k'.
+
+Goal forall s k k' m,
+ (pl k' (nexists (fun w => (nexists (fun b => pl (pair w w)
+ (pl (pair s b)
+ (nexists (fun w0 => (nexists (fun a => pl (pair b w0)
+ (nexists (fun w1 => (nexists (fun c => pl
+ (pair a w1) (pl (pair a c) k))))))))))))))) m.
+intros.
+eapply plImp; [ | eauto | intros ].
+2:econstructor.
+2:econstructor.
+2:eapply plImp; [ | eauto | intros ].
+3:eapply plImp; [ | eauto | intros ].
+4:econstructor.
+4:econstructor.
+4:eapply plImp; [ | eauto | intros ].
+5:econstructor.
+5:econstructor.
+5:eauto.
+4:eauto.
+3:eauto.
+2:eauto.
+
+assert (X := 1).
+clear X. (* very slow! *)
+
+simpl. (* exception Not_found *)
+
+Admitted.
diff --git a/test-suite/bugs/closed/shouldsucceed/1776.v b/test-suite/bugs/closed/shouldsucceed/1776.v
new file mode 100644
index 00000000..abf85455
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1776.v
@@ -0,0 +1,22 @@
+Axiom pair : nat -> nat -> nat -> Prop.
+Axiom pl : (nat -> Prop) -> (nat -> Prop) -> (nat -> Prop).
+Axiom plImpR : forall k P Q,
+ pl P Q k -> forall (Q':nat -> Prop),
+ (forall k', Q k' -> Q' k') ->
+ pl P Q' k.
+
+Definition nexists (P:nat -> nat -> Prop) : nat -> Prop :=
+ fun k' => exists k, P k k'.
+
+Goal forall a A m,
+ True ->
+ (pl A (nexists (fun x => (nexists
+ (fun y => pl (pair a (S x)) (pair a (S y))))))) m.
+Proof.
+ intros.
+ eapply plImpR; [ | intros; econstructor; econstructor; eauto].
+ clear H;
+ match goal with
+ | |- (pl _ (pl (pair _ ?x) _)) _ => replace x with 0
+ end.
+Admitted.
diff --git a/test-suite/bugs/closed/shouldsucceed/1779.v b/test-suite/bugs/closed/shouldsucceed/1779.v
new file mode 100644
index 00000000..95bb66b9
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1779.v
@@ -0,0 +1,25 @@
+Require Import Div2.
+
+Lemma double_div2: forall n, div2 (double n) = n.
+exact (fun n => let _subcase :=
+ let _cofact := fun _ : 0 = 0 => refl_equal 0 in
+ _cofact (let _fact := refl_equal 0 in _fact) in
+ let _subcase0 :=
+ fun (m : nat) (Hrec : div2 (double m) = m) =>
+ let _fact := f_equal div2 (double_S m) in
+ let _eq := trans_eq _fact (refl_equal (S (div2 (double m)))) in
+ let _eq0 :=
+ trans_eq _eq
+ (trans_eq
+ (f_equal (fun f : nat -> nat => f (div2 (double m)))
+ (refl_equal S)) (f_equal S Hrec)) in
+ _eq0 in
+ (fix _fix (__ : nat) : div2 (double __) = __ :=
+ match __ as n return (div2 (double n) = n) with
+ | 0 => _subcase
+ | S __0 =>
+ (fun _hrec : div2 (double __0) = __0 => _subcase0 __0 _hrec)
+ (_fix __0)
+ end) n).
+Guarded.
+Defined.
diff --git a/test-suite/bugs/closed/shouldsucceed/1784.v b/test-suite/bugs/closed/shouldsucceed/1784.v
new file mode 100644
index 00000000..616dd26f
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1784.v
@@ -0,0 +1,101 @@
+Require Import List.
+Require Import ZArith.
+Require String. Open Scope string_scope.
+Ltac Case s := let c := fresh "case" in set (c := s).
+
+Set Implicit Arguments.
+Unset Strict Implicit.
+
+Inductive sv : Set :=
+| I : Z -> sv
+| S : list sv -> sv.
+
+Section sv_induction.
+
+Variables
+ (VP: sv -> Prop)
+ (LP: list sv -> Prop)
+
+ (VPint: forall n, VP (I n))
+ (VPset: forall vs, LP vs -> VP (S vs))
+ (lpcons: forall v vs, VP v -> LP vs -> LP (v::vs))
+ (lpnil: LP nil).
+
+Fixpoint setl_value_indp (x:sv) {struct x}: VP x :=
+ match x as x return VP x with
+ | I n => VPint n
+ | S vs =>
+ VPset
+ ((fix values_indp (vs:list sv) {struct vs}: (LP vs) :=
+ match vs as vs return LP vs with
+ | nil => lpnil
+ | v::vs => lpcons (setl_value_indp v) (values_indp vs)
+ end) vs)
+ end.
+End sv_induction.
+
+Inductive slt : sv -> sv -> Prop :=
+| IC : forall z, slt (I z) (I z)
+| IS : forall vs vs', slist_in vs vs' -> slt (S vs) (S vs')
+
+with sin : sv -> list sv -> Prop :=
+| Ihd : forall s s' sv', slt s s' -> sin s (s'::sv')
+| Itl : forall s s' sv', sin s sv' -> sin s (s'::sv')
+
+with slist_in : list sv -> list sv -> Prop :=
+| Inil : forall sv',
+ slist_in nil sv'
+| Icons : forall s sv sv',
+ sin s sv' ->
+ slist_in sv sv' ->
+ slist_in (s::sv) sv'.
+
+Hint Constructors sin slt slist_in.
+
+Require Import Program.
+
+Program Fixpoint lt_dec (x y:sv) { struct x } : {slt x y}+{~slt x y} :=
+ match x with
+ | I x =>
+ match y with
+ | I y => if (Z_eq_dec x y) then in_left else in_right
+ | S ys => in_right
+ end
+ | S xs =>
+ match y with
+ | I y => in_right
+ | S ys =>
+ let fix list_in (xs ys:list sv) {struct xs} :
+ {slist_in xs ys} + {~slist_in xs ys} :=
+ match xs with
+ | nil => in_left
+ | x::xs =>
+ let fix elem_in (ys:list sv) : {sin x ys}+{~sin x ys} :=
+ match ys with
+ | nil => in_right
+ | y::ys => if lt_dec x y then in_left else if elem_in
+ ys then in_left else in_right
+ end
+ in
+ if elem_in ys then
+ if list_in xs ys then in_left else in_right
+ else in_right
+ end
+ in if list_in xs ys then in_left else in_right
+ end
+ end.
+
+Next Obligation. apply H; inversion H0; subst; trivial. Defined.
+Next Obligation. inversion H. Defined.
+Next Obligation. inversion H. Defined.
+Next Obligation. inversion H; subst. Defined.
+Next Obligation.
+ contradict H. inversion H1; subst. assumption.
+ contradict H0; assumption. Defined.
+Next Obligation.
+ contradict H0. inversion H1; subst. assumption. Defined.
+Next Obligation.
+ contradict H. inversion H0; subst. assumption. Defined.
+Next Obligation.
+ contradict H. inversion H0; subst; auto. Defined.
+
diff --git a/test-suite/bugs/closed/shouldsucceed/1844.v b/test-suite/bugs/closed/shouldsucceed/1844.v
new file mode 100644
index 00000000..545f2615
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1844.v
@@ -0,0 +1,217 @@
+Require Import ZArith.
+
+Definition zeq := Z_eq_dec.
+
+Definition update (A: Set) (x: Z) (v: A) (s: Z -> A) : Z -> A :=
+ fun y => if zeq x y then v else s y.
+
+Implicit Arguments update [A].
+
+Definition ident := Z.
+Parameter operator: Set.
+Parameter value: Set.
+Parameter is_true: value -> Prop.
+Definition label := Z.
+
+Inductive expr : Set :=
+ | Evar: ident -> expr
+ | Econst: value -> expr
+ | Eop: operator -> expr -> expr -> expr.
+
+Inductive stmt : Set :=
+ | Sskip: stmt
+ | Sassign: ident -> expr -> stmt
+ | Scall: ident -> ident -> expr -> stmt (* x := f(e) *)
+ | Sreturn: expr -> stmt
+ | Sseq: stmt -> stmt -> stmt
+ | Sifthenelse: expr -> stmt -> stmt -> stmt
+ | Sloop: stmt -> stmt
+ | Sblock: stmt -> stmt
+ | Sexit: nat -> stmt
+ | Slabel: label -> stmt -> stmt
+ | Sgoto: label -> stmt.
+
+Record function : Set := mkfunction {
+ fn_param: ident;
+ fn_body: stmt
+}.
+
+Parameter program: ident -> option function.
+
+Parameter main_function: ident.
+
+Definition store := ident -> value.
+
+Parameter empty_store : store.
+
+Parameter eval_op: operator -> value -> value -> option value.
+
+Fixpoint eval_expr (st: store) (e: expr) {struct e} : option value :=
+ match e with
+ | Evar v => Some (st v)
+ | Econst v => Some v
+ | Eop op e1 e2 =>
+ match eval_expr st e1, eval_expr st e2 with
+ | Some v1, Some v2 => eval_op op v1 v2
+ | _, _ => None
+ end
+ end.
+
+Inductive outcome: Set :=
+ | Onormal: outcome
+ | Oexit: nat -> outcome
+ | Ogoto: label -> outcome
+ | Oreturn: value -> outcome.
+
+Definition outcome_block (out: outcome) : outcome :=
+ match out with
+ | Onormal => Onormal
+ | Oexit O => Onormal
+ | Oexit (S m) => Oexit m
+ | Ogoto lbl => Ogoto lbl
+ | Oreturn v => Oreturn v
+ end.
+
+Fixpoint label_defined (lbl: label) (s: stmt) {struct s}: Prop :=
+ match s with
+ | Sskip => False
+ | Sassign id e => False
+ | Scall id fn e => False
+ | Sreturn e => False
+ | Sseq s1 s2 => label_defined lbl s1 \/ label_defined lbl s2
+ | Sifthenelse e s1 s2 => label_defined lbl s1 \/ label_defined lbl s2
+ | Sloop s1 => label_defined lbl s1
+ | Sblock s1 => label_defined lbl s1
+ | Sexit n => False
+ | Slabel lbl1 s1 => lbl1 = lbl \/ label_defined lbl s1
+ | Sgoto lbl => False
+ end.
+
+Inductive exec : stmt -> store -> outcome -> store -> Prop :=
+ | exec_skip: forall st,
+ exec Sskip st Onormal st
+ | exec_assign: forall id e st v,
+ eval_expr st e = Some v ->
+ exec (Sassign id e) st Onormal (update id v st)
+ | exec_call: forall id fn e st v1 f v2 st',
+ eval_expr st e = Some v1 ->
+ program fn = Some f ->
+ exec_function f (update f.(fn_param) v1 empty_store) v2 st' ->
+ exec (Scall id fn e) st Onormal (update id v2 st)
+ | exec_return: forall e st v,
+ eval_expr st e = Some v ->
+ exec (Sreturn e) st (Oreturn v) st
+ | exec_seq_2: forall s1 s2 st st1 out' st',
+ exec s1 st Onormal st1 -> exec s2 st1 out' st' ->
+ exec (Sseq s1 s2) st out' st'
+ | exec_seq_1: forall s1 s2 st out st',
+ exec s1 st out st' -> out <> Onormal ->
+ exec (Sseq s1 s2) st out st'
+ | exec_ifthenelse_true: forall e s1 s2 st out st' v,
+ eval_expr st e = Some v -> is_true v -> exec s1 st out st' ->
+ exec (Sifthenelse e s1 s2) st out st'
+ | exec_ifthenelse_false: forall e s1 s2 st out st' v,
+ eval_expr st e = Some v -> ~is_true v -> exec s2 st out st' ->
+ exec (Sifthenelse e s1 s2) st out st'
+ | exec_loop_loop: forall s st st1 out' st',
+ exec s st Onormal st1 ->
+ exec (Sloop s) st1 out' st' ->
+ exec (Sloop s) st out' st'
+ | exec_loop_stop: forall s st st' out,
+ exec s st out st' -> out <> Onormal ->
+ exec (Sloop s) st out st'
+ | exec_block: forall s st out st',
+ exec s st out st' ->
+ exec (Sblock s) st (outcome_block out) st'
+ | exec_exit: forall n st,
+ exec (Sexit n) st (Oexit n) st
+ | exec_label: forall s lbl st st' out,
+ exec s st out st' ->
+ exec (Slabel lbl s) st out st'
+ | exec_goto: forall st lbl,
+ exec (Sgoto lbl) st (Ogoto lbl) st
+
+(** [execg lbl stmt st out st'] starts executing at label [lbl] within [s],
+ in initial store [st]. The result of the execution is the outcome
+ [out] with final store [st']. *)
+
+with execg: label -> stmt -> store -> outcome -> store -> Prop :=
+ | execg_left_seq_2: forall lbl s1 s2 st st1 out' st',
+ execg lbl s1 st Onormal st1 -> exec s2 st1 out' st' ->
+ execg lbl (Sseq s1 s2) st out' st'
+ | execg_left_seq_1: forall lbl s1 s2 st out st',
+ execg lbl s1 st out st' -> out <> Onormal ->
+ execg lbl (Sseq s1 s2) st out st'
+ | execg_right_seq: forall lbl s1 s2 st out st',
+ ~(label_defined lbl s1) ->
+ execg lbl s2 st out st' ->
+ execg lbl (Sseq s1 s2) st out st'
+ | execg_ifthenelse_left: forall lbl e s1 s2 st out st',
+ execg lbl s1 st out st' ->
+ execg lbl (Sifthenelse e s1 s2) st out st'
+ | execg_ifthenelse_right: forall lbl e s1 s2 st out st',
+ ~(label_defined lbl s1) ->
+ execg lbl s2 st out st' ->
+ execg lbl (Sifthenelse e s1 s2) st out st'
+ | execg_loop_loop: forall lbl s st st1 out' st',
+ execg lbl s st Onormal st1 ->
+ exec (Sloop s) st1 out' st' ->
+ execg lbl (Sloop s) st out' st'
+ | execg_loop_stop: forall lbl s st st' out,
+ execg lbl s st out st' -> out <> Onormal ->
+ execg lbl (Sloop s) st out st'
+ | execg_block: forall lbl s st out st',
+ execg lbl s st out st' ->
+ execg lbl (Sblock s) st (outcome_block out) st'
+ | execg_label_found: forall lbl s st st' out,
+ exec s st out st' ->
+ execg lbl (Slabel lbl s) st out st'
+ | execg_label_notfound: forall lbl s lbl' st st' out,
+ lbl' <> lbl ->
+ execg lbl s st out st' ->
+ execg lbl (Slabel lbl' s) st out st'
+
+(** [exec_finish out st st'] takes the outcome [out] and the store [st]
+ at the end of the evaluation of the program. If [out] is a [goto],
+ execute again the program starting at the corresponding label.
+ Iterate this way until [out] is [Onormal]. *)
+
+with exec_finish: function -> outcome -> store -> value -> store -> Prop :=
+ | exec_finish_normal: forall f st v,
+ exec_finish f (Oreturn v) st v st
+ | exec_finish_goto: forall f lbl st out v st1 st',
+ execg lbl f.(fn_body) st out st1 ->
+ exec_finish f out st1 v st' ->
+ exec_finish f (Ogoto lbl) st v st'
+
+(** Execution of a function *)
+
+with exec_function: function -> store -> value -> store -> Prop :=
+ | exec_function_intro: forall f st out st1 v st',
+ exec f.(fn_body) st out st1 ->
+ exec_finish f out st1 v st' ->
+ exec_function f st v st'.
+
+Scheme exec_ind4:= Minimality for exec Sort Prop
+ with execg_ind4:= Minimality for execg Sort Prop
+ with exec_finish_ind4 := Minimality for exec_finish Sort Prop
+ with exec_function_ind4 := Minimality for exec_function Sort Prop.
+
+Scheme exec_dind4:= Induction for exec Sort Prop
+ with execg_dind4:= Minimality for execg Sort Prop
+ with exec_finish_dind4 := Induction for exec_finish Sort Prop
+ with exec_function_dind4 := Induction for exec_function Sort Prop.
+
+Combined Scheme exec_inductiond from exec_dind4, execg_dind4, exec_finish_dind4,
+ exec_function_dind4.
+
+Scheme exec_dind4' := Induction for exec Sort Prop
+ with execg_dind4' := Induction for execg Sort Prop
+ with exec_finish_dind4' := Induction for exec_finish Sort Prop
+ with exec_function_dind4' := Induction for exec_function Sort Prop.
+
+Combined Scheme exec_induction from exec_ind4, execg_ind4, exec_finish_ind4,
+ exec_function_ind4.
+
+Combined Scheme exec_inductiond' from exec_dind4', execg_dind4', exec_finish_dind4',
+ exec_function_dind4'.
diff --git a/test-suite/bugs/closed/shouldsucceed/1865.v b/test-suite/bugs/closed/shouldsucceed/1865.v
new file mode 100644
index 00000000..17c19989
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/1865.v
@@ -0,0 +1,18 @@
+(* Check that tactics (here dependent inversion) do not generate
+ conversion problems T <= U with sup's of universes in U *)
+
+(* Submitted by David Nowak *)
+
+Inductive list (A:Set) : nat -> Set :=
+| nil : list A O
+| cons : forall n, A -> list A n -> list A (S n).
+
+Definition f (n:nat) : Type :=
+ match n with
+ | O => bool
+ | _ => unit
+ end.
+
+Goal forall A n, list A n -> f n.
+intros A n.
+dependent inversion n.
diff --git a/test-suite/bugs/closed/shouldsucceed/348.v b/test-suite/bugs/closed/shouldsucceed/348.v
new file mode 100644
index 00000000..28cc5cb1
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/348.v
@@ -0,0 +1,13 @@
+Module Type S.
+ Parameter empty: Set.
+End S.
+
+Module D (M:S).
+ Import M.
+ Definition empty:=nat.
+End D.
+
+Module D' (M:S).
+ Import M.
+ Definition empty:Set. exact nat. Save.
+End D'.
diff --git a/test-suite/bugs/closed/shouldsucceed/38.v b/test-suite/bugs/closed/shouldsucceed/38.v
new file mode 100644
index 00000000..7bc04b1f
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/38.v
@@ -0,0 +1,22 @@
+Require Import Setoid.
+
+Variable A : Set.
+
+Inductive liste : Set :=
+| vide : liste
+| c : A -> liste -> liste.
+
+Inductive e : A -> liste -> Prop :=
+| ec : forall (x : A) (l : liste), e x (c x l)
+| ee : forall (x y : A) (l : liste), e x l -> e x (c y l).
+
+Definition same := fun (l m : liste) => forall (x : A), e x l <-> e x m.
+
+Definition same_refl (x:liste) : (same x x).
+ unfold same; split; intros; trivial.
+Save.
+
+Goal forall (x:liste), (same x x).
+ intro.
+ apply (same_refl x).
+Qed.
diff --git a/test-suite/bugs/closed/shouldsucceed/545.v b/test-suite/bugs/closed/shouldsucceed/545.v
new file mode 100644
index 00000000..926af7dd
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/545.v
@@ -0,0 +1,5 @@
+Require Export Reals.
+
+Parameter toto : nat -> nat -> nat.
+
+Notation " e # f " := (toto e f) (at level 30, f at level 0).
diff --git a/test-suite/bugs/closed/shouldsucceed/846.v b/test-suite/bugs/closed/shouldsucceed/846.v
new file mode 100644
index 00000000..a963b225
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/846.v
@@ -0,0 +1,213 @@
+Set Implicit Arguments.
+
+Open Scope type_scope.
+
+Inductive One : Set := inOne: One.
+
+Definition maybe: forall A B:Set,(A -> B) -> One + A -> One + B.
+Proof.
+ intros A B f c.
+ case c.
+ left; assumption.
+ right; apply f; assumption.
+Defined.
+
+Definition id (A:Set)(a:A):=a.
+
+Definition LamF (X: Set -> Set)(A:Set) :Set :=
+ A + (X A)*(X A) + X(One + A).
+
+Definition LamF' (X: Set -> Set)(A:Set) :Set :=
+ LamF X A.
+
+Require Import List.
+Require Import Bool.
+
+Definition index := list bool.
+
+Inductive L (A:Set) : index -> Set :=
+ initL: A -> L A nil
+ | pluslL: forall l:index, One -> L A (false::l)
+ | plusrL: forall l:index, L A l -> L A (false::l)
+ | varL: forall l:index, L A l -> L A (true::l)
+ | appL: forall l:index, L A (true::l) -> L A (true::l) -> L A (true::l)
+ | absL: forall l:index, L A (true::false::l) -> L A (true::l).
+
+Scheme L_rec_simp := Minimality for L Sort Set.
+
+Definition Lam' (A:Set) := L A (true::nil).
+
+Definition aczelapp: forall (l1 l2: index)(A:Set), L (L A l2) l1 -> L A
+ (l1++l2).
+Proof.
+ intros l1 l2 A.
+ generalize l1.
+ clear l1.
+ (* Check (fun i:index => L A (i++l2)). *)
+ apply (L_rec_simp (A:=L A l2) (fun i:index => L A (i++l2))).
+ trivial.
+ intros l o.
+ simpl app.
+ apply pluslL; assumption.
+ intros l _ t.
+ simpl app.
+ apply plusrL; assumption.
+ intros l _ t.
+ simpl app.
+ apply varL; assumption.
+ intros l _ t1 _ t2.
+ simpl app in *|-*.
+ Check 0.
+ apply appL; [exact t1| exact t2].
+ intros l _ t.
+ simpl app in *|-*.
+ Check 0.
+ apply absL; assumption.
+Defined.
+
+Definition monL: forall (l:index)(A:Set)(B:Set), (A->B) -> L A l -> L B l.
+Proof.
+ intros l A B f.
+ intro t.
+ elim t.
+ intro a.
+ exact (initL (f a)).
+ intros i u.
+ exact (pluslL _ _ u).
+ intros i _ r.
+ exact (plusrL r).
+ intros i _ r.
+ exact (varL r).
+ intros i _ r1 _ r2.
+ exact (appL r1 r2).
+ intros i _ r.
+ exact (absL r).
+Defined.
+
+Definition lam': forall (A B:Set), (A -> B) -> Lam' A -> Lam' B.
+Proof.
+ intros A B f t.
+ unfold Lam' in *|-*.
+ Check 0.
+ exact (monL f t).
+Defined.
+
+Definition inLam': forall A:Set, LamF' Lam' A -> Lam' A.
+Proof.
+ intros A [[a|[t1 t2]]|r].
+ unfold Lam'.
+ exact (varL (initL a)).
+ exact (appL t1 t2).
+ unfold Lam' in * |- *.
+ Check 0.
+ apply absL.
+ change (L A ((true::nil) ++ (false::nil))).
+ apply aczelapp.
+ (* Check (fun x:One + A => (match (maybe (fun a:A => initL a) x) with
+ | inl u => pluslL _ _ u
+ | inr t' => plusrL t' end)). *)
+ exact (monL (fun x:One + A =>
+ (match (maybe (fun a:A => initL a) x) with
+ | inl u => pluslL _ _ u
+ | inr t' => plusrL t' end)) r).
+Defined.
+
+Section minimal.
+
+Definition sub1 (F G: Set -> Set):= forall A:Set, F A->G A.
+Hypothesis G: Set -> Set.
+Hypothesis step: sub1 (LamF' G) G.
+
+Fixpoint L'(A:Set)(i:index){struct i} : Set :=
+ match i with
+ nil => A
+ | false::l => One + L' A l
+ | true::l => G (L' A l)
+ end.
+
+Definition LinL': forall (A:Set)(i:index), L A i -> L' A i.
+Proof.
+ intros A i t.
+ elim t.
+ intro a.
+ unfold L'.
+ assumption.
+ intros l u.
+ left; assumption.
+ intros l _ r.
+ right; assumption.
+ intros l _ r.
+ apply (step (A:=L' A l)).
+ exact (inl _ (inl _ r)).
+ intros l _ r1 _ r2.
+ apply (step (A:=L' A l)).
+ (* unfold L' in * |- *.
+ Check 0. *)
+ exact (inl _ (inr _ (pair r1 r2))).
+ intros l _ r.
+ apply (step (A:=L' A l)).
+ exact (inr _ r).
+Defined.
+
+Definition L'inG: forall A: Set, L' A (true::nil) -> G A.
+Proof.
+ intros A t.
+ unfold L' in t.
+ assumption.
+Defined.
+
+Definition Itbasic: sub1 Lam' G.
+Proof.
+ intros A t.
+ apply L'inG.
+ unfold Lam' in t.
+ exact (LinL' t).
+Defined.
+
+End minimal.
+
+Definition recid := Itbasic inLam'.
+
+Definition L'Lam'inL: forall (i:index)(A:Set), L' Lam' A i -> L A i.
+Proof.
+ intros i A t.
+ induction i.
+ unfold L' in t.
+ apply initL.
+ assumption.
+ induction a.
+ simpl L' in t.
+ apply (aczelapp (l1:=true::nil) (l2:=i)).
+ exact (lam' IHi t).
+ simpl L' in t.
+ induction t.
+ exact (pluslL _ _ a).
+ exact (plusrL (IHi b)).
+Defined.
+
+
+Lemma recidgen: forall(A:Set)(i:index)(t:L A i), L'Lam'inL i A (LinL' inLam' t)
+ = t.
+Proof.
+ intros A i t.
+ induction t.
+ trivial.
+ trivial.
+ simpl.
+ rewrite IHt.
+ trivial.
+ simpl L'Lam'inL.
+ rewrite IHt.
+ trivial.
+ simpl L'Lam'inL.
+ simpl L'Lam'inL in IHt1.
+ unfold lam' in IHt1.
+ simpl L'Lam'inL in IHt2.
+ unfold lam' in IHt2.
+
+ (* going on. This fails for the original solution. *)
+ rewrite IHt1.
+ rewrite IHt2.
+ trivial.
+Abort. (* one goal still left *)
+
diff --git a/test-suite/bugs/closed/shouldsucceed/931.v b/test-suite/bugs/closed/shouldsucceed/931.v
new file mode 100644
index 00000000..21f15e72
--- /dev/null
+++ b/test-suite/bugs/closed/shouldsucceed/931.v
@@ -0,0 +1,7 @@
+Parameter P : forall n : nat, n=n -> Prop.
+
+Goal Prop.
+ refine (P _ _).
+ instantiate (1:=0).
+ trivial.
+Qed.
diff --git a/test-suite/bugs/opened/1773.v b/test-suite/bugs/opened/1773.v
new file mode 100644
index 00000000..4aabf19c
--- /dev/null
+++ b/test-suite/bugs/opened/1773.v
@@ -0,0 +1,10 @@
+Goal forall B C : nat -> nat -> Prop, forall k, C 0 k ->
+ (exists A, (forall k', C A k' -> B A k') -> B A k).
+Proof.
+ intros B C k H.
+ econstructor.
+ intros X.
+ apply X.
+ apply H.
+Qed.
+
diff --git a/test-suite/bugs/opened/shouldnotfail/1338.v-disabled b/test-suite/bugs/opened/shouldnotfail/1338.v-disabled
new file mode 100644
index 00000000..f383d534
--- /dev/null
+++ b/test-suite/bugs/opened/shouldnotfail/1338.v-disabled
@@ -0,0 +1,12 @@
+Require Import Omega.
+
+Goal forall x, 0 <= x -> x <= 20 ->
+x <> 0
+ -> x <> 1 -> x <> 2 -> x <> 3 -> x <>4 -> x <> 5 -> x <> 6 -> x <> 7 -> x <> 8
+-> x <> 9 -> x <> 10
+ -> x <> 11 -> x <> 12 -> x <> 13 -> x <> 14 -> x <> 15 -> x <> 16 -> x <> 17
+-> x <> 18 -> x <> 19 -> x <> 20 -> False.
+Proof.
+ intros.
+ omega.
+Qed.
diff --git a/test-suite/bugs/opened/shouldnotfail/1416.v b/test-suite/bugs/opened/shouldnotfail/1416.v
new file mode 100644
index 00000000..c6f4302d
--- /dev/null
+++ b/test-suite/bugs/opened/shouldnotfail/1416.v
@@ -0,0 +1,27 @@
+Set Implicit Arguments.
+
+Record Place (Env A: Type) : Type := {
+ read: Env -> A ;
+ write: Env -> A -> Env ;
+ write_read: forall (e:Env), (write e (read e))=e
+}.
+
+Hint Rewrite -> write_read: placeeq.
+
+Record sumPl (Env A B: Type) (vL:(Place Env A)) (vR:(Place Env B)) : Type :=
+ {
+ mkEnv: A -> B -> Env ;
+ mkEnv2writeL: forall (e:Env) (x:A), (mkEnv x (read vR e))=(write vL e x)
+ }.
+
+(* when the following line is commented, the bug does not appear *)
+Hint Rewrite -> mkEnv2writeL: placeeq.
+
+Lemma autorewrite_raise_anomaly: forall (Env A:Type) (e: Env) (p:Place Env A),
+ (exists e1:Env, e=(write p e1 (read p e))).
+Proof.
+ intros Env A e p; eapply ex_intro.
+ autorewrite with placeeq. (* Here is the bug *)
+ auto.
+Qed.
+
diff --git a/test-suite/bugs/opened/shouldnotfail/1501.v b/test-suite/bugs/opened/shouldnotfail/1501.v
new file mode 100644
index 00000000..85c09dbd
--- /dev/null
+++ b/test-suite/bugs/opened/shouldnotfail/1501.v
@@ -0,0 +1,93 @@
+Set Implicit Arguments.
+
+
+Require Export Relation_Definitions.
+Require Export Setoid.
+
+
+Section Essais.
+
+(* Parametrized Setoid *)
+Parameter K : Type -> Type.
+Parameter equiv : forall A : Type, K A -> K A -> Prop.
+Parameter equiv_refl : forall (A : Type) (x : K A), equiv x x.
+Parameter equiv_sym : forall (A : Type) (x y : K A), equiv x y -> equiv y x.
+Parameter equiv_trans : forall (A : Type) (x y z : K A), equiv x y -> equiv y z
+-> equiv x z.
+
+(* basic operations *)
+Parameter val : forall A : Type, A -> K A.
+Parameter bind : forall A B : Type, K A -> (A -> K B) -> K B.
+
+Parameter
+ bind_compat :
+ forall (A B : Type) (m1 m2 : K A) (f1 f2 : A -> K B),
+ equiv m1 m2 ->
+ (forall x : A, equiv (f1 x) (f2 x)) -> equiv (bind m1 f1) (bind m2 f2).
+
+(* monad axioms *)
+Parameter
+ bind_val_l :
+ forall (A B : Type) (a : A) (f : A -> K B), equiv (bind (val a) f) (f a).
+Parameter
+ bind_val_r :
+ forall (A : Type) (m : K A), equiv (bind m (fun a => val a)) m.
+Parameter
+ bind_assoc :
+ forall (A B C : Type) (m : K A) (f : A -> K B) (g : B -> K C),
+ equiv (bind (bind m f) g) (bind m (fun a => bind (f a) g)).
+
+
+Hint Resolve equiv_refl equiv_sym equiv_trans: monad.
+
+Add Relation K equiv
+ reflexivity proved by (@equiv_refl)
+ symmetry proved by (@equiv_sym)
+ transitivity proved by (@equiv_trans)
+ as equiv_rel.
+
+Definition fequiv (A B: Type) (f g: A -> K B) := forall (x:A), (equiv (f x) (g
+x)).
+
+Lemma fequiv_refl : forall (A B: Type) (f : A -> K B), fequiv f f.
+Proof.
+ unfold fequiv; auto with monad.
+Qed.
+
+Lemma fequiv_sym : forall (A B: Type) (x y : A -> K B), fequiv x y -> fequiv y
+x.
+Proof.
+ unfold fequiv; auto with monad.
+Qed.
+
+Lemma fequiv_trans : forall (A B: Type) (x y z : A -> K B), fequiv x y ->
+fequiv
+y z -> fequiv x z.
+Proof.
+ unfold fequiv; intros; eapply equiv_trans; auto with monad.
+Qed.
+
+Add Relation (fun (A B:Type) => A -> K B) fequiv
+ reflexivity proved by (@fequiv_refl)
+ symmetry proved by (@fequiv_sym)
+ transitivity proved by (@fequiv_trans)
+ as fequiv_rel.
+
+Add Morphism bind
+ with signature equiv ==> fequiv ==> equiv
+ as bind_mor.
+Proof.
+ unfold fequiv; intros; apply bind_compat; auto.
+Qed.
+
+Lemma test:
+ forall (A B: Type) (m1 m2 m3: K A) (f: A -> A -> K B),
+ (equiv m1 m2) -> (equiv m2 m3) ->
+ equiv (bind m1 (fun a => bind m2 (fun a' => f a a')))
+ (bind m2 (fun a => bind m3 (fun a' => f a a'))).
+Proof.
+ intros A B m1 m2 m3 f H1 H2.
+ setoid_rewrite H1. (* this works *)
+ setoid_rewrite H2.
+ trivial by equiv_refl.
+Qed.
diff --git a/test-suite/bugs/opened/shouldnotfail/1596.v b/test-suite/bugs/opened/shouldnotfail/1596.v
new file mode 100644
index 00000000..766bf524
--- /dev/null
+++ b/test-suite/bugs/opened/shouldnotfail/1596.v
@@ -0,0 +1,242 @@
+
+Require Import Relations.
+Require Import FSets.
+Require Import Arith.
+
+Lemma Bool_elim_bool : forall (b:bool),b=true \/ b=false.
+ destruct b;try tauto.
+Qed.
+
+Module OrderedPair (X:OrderedType) (Y:OrderedType) <: OrderedType with
+Definition t := (X.t * Y.t)%type.
+ Definition t := (X.t * Y.t)%type.
+
+ Definition eq (xy1:t) (xy2:t) :=
+ let (x1,y1) := xy1 in
+ let (x2,y2) := xy2 in
+ (X.eq x1 x2) /\ (Y.eq y1 y2).
+
+ Definition lt (xy1:t) (xy2:t) :=
+ let (x1,y1) := xy1 in
+ let (x2,y2) := xy2 in
+ (X.lt x1 x2) \/ ((X.eq x1 x2) /\ (Y.lt y1 y2)).
+
+ Lemma eq_refl : forall (x:t),(eq x x).
+ destruct x.
+ unfold eq.
+ split;[apply X.eq_refl | apply Y.eq_refl].
+ Qed.
+
+ Lemma eq_sym : forall (x y:t),(eq x y)->(eq y x).
+ destruct x;destruct y;unfold eq;intro.
+ elim H;clear H;intros.
+ split;[apply X.eq_sym | apply Y.eq_sym];trivial.
+ Qed.
+
+ Lemma eq_trans : forall (x y z:t),(eq x y)->(eq y z)->(eq x z).
+ unfold eq;destruct x;destruct y;destruct z;intros.
+ elim H;clear H;intros.
+ elim H0;clear H0;intros.
+ split;[eapply X.eq_trans | eapply Y.eq_trans];eauto.
+ Qed.
+
+ Lemma lt_trans : forall (x y z:t),(lt x y)->(lt y z)->(lt x z).
+ unfold lt;destruct x;destruct y;destruct z;intros.
+ case H;clear H;intro.
+ case H0;clear H0;intro.
+ left.
+ eapply X.lt_trans;eauto.
+ elim H0;clear H0;intros.
+ left.
+ case (X.compare t0 t4);trivial;intros.
+ generalize (X.eq_sym H0);intro.
+ generalize (X.eq_trans e H2);intro.
+ elim (X.lt_not_eq H H3).
+ generalize (X.lt_trans l H);intro.
+ generalize (X.eq_sym H0);intro.
+ elim (X.lt_not_eq H2 H3).
+ elim H;clear H;intros.
+ case H0;clear H0;intro.
+ left.
+ case (X.compare t0 t4);trivial;intros.
+ generalize (X.eq_sym H);intro.
+ generalize (X.eq_trans H2 e);intro.
+ elim (X.lt_not_eq H0 H3).
+ generalize (X.lt_trans H0 l);intro.
+ generalize (X.eq_sym H);intro.
+ elim (X.lt_not_eq H2 H3).
+ elim H0;clear H0;intros.
+ right.
+ split.
+ eauto.
+ eauto.
+ Qed.
+
+ Lemma lt_not_eq : forall (x y:t),(lt x y)->~(eq x y).
+ unfold lt, eq;destruct x;destruct y;intro;intro.
+ elim H0;clear H0;intros.
+ case H.
+ intro.
+ apply (X.lt_not_eq H2 H0).
+ intro.
+ elim H2;clear H2;intros.
+ apply (Y.lt_not_eq H3 H1).
+ Qed.
+
+ Definition compare : forall (x y:t),(Compare lt eq x y).
+ destruct x;destruct y.
+ case (X.compare t0 t2);intro.
+ apply LT.
+ left;trivial.
+ case (Y.compare t1 t3);intro.
+ apply LT.
+ right.
+ tauto.
+ apply EQ.
+ split;trivial.
+ apply GT.
+ right;auto.
+ apply GT.
+ left;trivial.
+ Defined.
+
+ Hint Immediate eq_sym.
+ Hint Resolve eq_refl eq_trans lt_not_eq lt_trans.
+End OrderedPair.
+
+Module MessageSpi.
+ Inductive message : Set :=
+ | MNam : nat -> message.
+
+ Definition t := message.
+
+ Fixpoint message_lt (m n:message) {struct m} : Prop :=
+ match (m,n) with
+ | (MNam n1,MNam n2) => n1 < n2
+ end.
+
+ Module Ord <: OrderedType with Definition t := message with Definition eq :=
+@eq message.
+ Definition t := message.
+ Definition eq := @eq message.
+ Definition lt := message_lt.
+
+ Lemma eq_refl : forall (x:t),eq x x.
+ unfold eq;auto.
+ Qed.
+
+ Lemma eq_sym : forall (x y:t),(eq x y )->(eq y x).
+ unfold eq;auto.
+ Qed.
+
+ Lemma eq_trans : forall (x y z:t),(eq x y)->(eq y z)->(eq x z).
+ unfold eq;auto;intros;congruence.
+ Qed.
+
+ Lemma lt_trans : forall (x y z:t),(lt x y)->(lt y z)->(lt x z).
+ unfold lt.
+ induction x;destruct y;simpl;try tauto;destruct z;try tauto;intros.
+ omega.
+ Qed.
+
+ Lemma lt_not_eq : forall (x y:t),(lt x y)->~(eq x y).
+ unfold eq;unfold lt.
+ induction x;destruct y;simpl;try tauto;intro;red;intro;try (discriminate
+H0);injection H0;intros.
+ elim (lt_irrefl n);try omega.
+ Qed.
+
+ Definition compare : forall (x y:t),(Compare lt eq x y).
+ unfold lt, eq.
+ induction x;destruct y;intros;try (apply LT;simpl;trivial;fail);try
+(apply
+GT;simpl;trivial;fail).
+ case (lt_eq_lt_dec n n0);intros;try (case s;clear s;intros).
+ apply LT;trivial.
+ apply EQ;trivial.
+ rewrite e;trivial.
+ apply GT;trivial.
+ Defined.
+
+ Hint Immediate eq_sym.
+ Hint Resolve eq_refl eq_trans lt_not_eq lt_trans.
+ End Ord.
+
+ Theorem eq_dec : forall (m n:message),{m=n}+{~(m=n)}.
+ intros.
+ case (Ord.compare m n);intro;[right | left | right];try (red;intro).
+ elim (Ord.lt_not_eq m n);auto.
+ rewrite e;auto.
+ elim (Ord.lt_not_eq n m);auto.
+ Defined.
+End MessageSpi.
+
+Module MessagePair := OrderedPair MessageSpi.Ord MessageSpi.Ord.
+
+Module Type Hedge := FSetInterface.S with Module E := MessagePair.
+
+Module A (H:Hedge).
+ Definition hedge := H.t.
+
+ Definition message_relation := relation MessageSpi.message.
+
+ Definition relation_of_hedge (h:hedge) (m n:MessageSpi.message) := H.In (m,n)
+h.
+
+ Inductive hedge_synthesis_relation (h:message_relation) : message_relation :=
+ | SynInc : forall (m n:MessageSpi.message),(h m
+n)->(hedge_synthesis_relation h m n).
+
+ Fixpoint hedge_in_synthesis (h:hedge) (m:MessageSpi.message)
+(n:MessageSpi.message) {struct m} : bool :=
+ if H.mem (m,n) h
+ then true
+ else false.
+
+ Definition hedge_synthesis_spec (h:hedge) := hedge_synthesis_relation
+(relation_of_hedge h).
+
+ Lemma hedge_in_synthesis_impl_hedge_synthesis_spec : forall (h:hedge),forall
+(m n:MessageSpi.message),(hedge_in_synthesis h m n)=true->(hedge_synthesis_spec
+h m n).
+ unfold hedge_synthesis_spec;unfold relation_of_hedge.
+ induction m;simpl;intro.
+ elim (Bool_elim_bool (H.mem (MessageSpi.MNam n,n0) h));intros.
+ apply SynInc;apply H.mem_2;trivial.
+ rewrite H in H0. (* !! possible here !! *)
+ discriminate H0.
+ Qed.
+End A.
+
+Module B (H:Hedge).
+ Definition hedge := H.t.
+
+ Definition message_relation := relation MessageSpi.t.
+
+ Definition relation_of_hedge (h:hedge) (m n:MessageSpi.t) := H.In (m,n) h.
+
+ Inductive hedge_synthesis_relation (h:message_relation) : message_relation :=
+ | SynInc : forall (m n:MessageSpi.t),(h m n)->(hedge_synthesis_relation h m
+n).
+
+ Fixpoint hedge_in_synthesis (h:hedge) (m:MessageSpi.t) (n:MessageSpi.t)
+{struct m} : bool :=
+ if H.mem (m,n) h
+ then true
+ else false.
+
+ Definition hedge_synthesis_spec (h:hedge) := hedge_synthesis_relation
+(relation_of_hedge h).
+
+ Lemma hedge_in_synthesis_impl_hedge_synthesis_spec : forall (h:hedge),forall
+(m n:MessageSpi.t),(hedge_in_synthesis h m n)=true->(hedge_synthesis_spec h m
+n).
+ unfold hedge_synthesis_spec;unfold relation_of_hedge.
+ induction m;simpl;intro.
+ elim (Bool_elim_bool (H.mem (MessageSpi.MNam n,n0) h));intros.
+ apply SynInc;apply H.mem_2;trivial.
+
+ rewrite H in H0. (* !! impossible here !! *)
+ discriminate H0.
+ Qed.
+End B. \ No newline at end of file
diff --git a/test-suite/bugs/opened/shouldnotfail/1811.v b/test-suite/bugs/opened/shouldnotfail/1811.v
new file mode 100644
index 00000000..037b7cb2
--- /dev/null
+++ b/test-suite/bugs/opened/shouldnotfail/1811.v
@@ -0,0 +1,9 @@
+Require Export Bool.
+
+Lemma neg2xor : forall b, xorb true b = negb b.
+Proof. auto. Qed.
+
+Goal forall b1 b2, (negb b1 = b2) -> xorb true b1 = b2.
+Proof.
+ intros b1 b2.
+ rewrite neg2xor. \ No newline at end of file
diff --git a/test-suite/bugs/opened/shouldnotfail/743.v b/test-suite/bugs/opened/shouldnotfail/743.v
new file mode 100644
index 00000000..f1eee6c1
--- /dev/null
+++ b/test-suite/bugs/opened/shouldnotfail/743.v
@@ -0,0 +1,12 @@
+Require Import Omega.
+
+Lemma foo : forall n m : Z, (n >= 0)%Z -> (n * m >= 0)%Z -> (n <= n + n * m)%Z.
+Proof.
+ intros. omega.
+Qed.
+
+Lemma foo' : forall n m : nat, n <= n + n * m.
+Proof.
+ intros. omega.
+Qed.
+
diff --git a/test-suite/check b/test-suite/check
index 504e96cc..f2307d40 100755
--- a/test-suite/check
+++ b/test-suite/check
@@ -106,6 +106,7 @@ test_interactive() {
# La fonction suivante teste en interactif
# It expects a line "(* Expected time < XXX.YYs *)" in the .v file
# with exactly two digits after the dot
+# The reference for time is a 6120 bogomips cpu
test_complexity() {
if [ -f /proc/cpuinfo ]; then
if grep -q bogomips /proc/cpuinfo; then # i386, ppc
@@ -145,28 +146,119 @@ test_complexity() {
fi
}
+test_bugs () {
+ # Process verifications concerning submitted bugs. A message is
+ # printed for all opened bugs (still active or seems to be closed).
+ # For closed bugs that behave as expected, no message is printed
+
+ # All files are assumed to have <# of the bug>.v as a name
+
+ echo "Testing opened bugs..."
+ # We first test opened bugs that should not succeed
+ files=`/bin/ls -1 $1/opened/shoulnotsucceed/*.v 2> /dev/null`
+ for f in $files; do
+ nbtests=`expr $nbtests + 1`
+ printf " "$f"..."
+ $command $f $2 > /dev/null 2>&1
+ if [ $? = 0 ]; then
+ echo "still active"
+ nbtestsok=`expr $nbtestsok + 1`
+ else
+ echo "Error! (bug seems to be closed, please check)"
+ fi
+ done
+
+ # And opened bugs that should not fail
+ files=`/bin/ls -1 $1/opened/shouldnotfail/*.v 2> /dev/null`
+ for f in $files; do
+ nbtests=`expr $nbtests + 1`
+ printf " "$f"..."
+ $command $f > /dev/null 2>&1
+ if [ $? != 0 ]; then
+ echo "still active"
+ nbtestsok=`expr $nbtestsok + 1`
+ else
+ echo "Error! (bug seems to be closed, please check)"
+ fi
+ done
+
+ echo "Testing closed bugs..."
+ # Then closed bugs that should succeed
+ files=`/bin/ls -1 $1/closed/shouldsucceed/*.v 2> /dev/null`
+ for f in $files; do
+ nbtests=`expr $nbtests + 1`
+ printf " "$f"..."
+ $command $f $2 > /dev/null 2>&1
+ if [ $? = 0 ]; then
+ echo "Ok"
+ nbtestsok=`expr $nbtestsok + 1`
+ else
+ echo "Error! (bug seems to be opened, please check)"
+ fi
+ done
+
+
+ # At last, we test closed bugs that should fail
+ files=`/bin/ls -1 $1/closed/shouldfail/*.v 2> /dev/null`
+ for f in $files; do
+ nbtests=`expr $nbtests + 1`
+ printf " "$f"..."
+ $command $f > /dev/null 2>&1
+ if [ $? != 0 ]; then
+ echo "Ok"
+ nbtestsok=`expr $nbtestsok + 1`
+ else
+ echo "Error! (bug seems to be opened, please check)"
+ fi
+ done
+
+}
+
+test_features () {
+ # Process verifications concerning submitted bugs. A message is
+ # printed for all opened bugs (still active or seem to be closed.
+ # For closed bugs that behave as expected, no message is printed
+
+ echo "Testing wishes..."
+ files=`/bin/ls -1 $1/*.v 2> /dev/null`
+ for f in $files; do
+ nbtests=`expr $nbtests + 1`
+ printf " "$f"..."
+ $command $f $2 > /dev/null 2>&1
+ if [ $? != 0 ]; then
+ echo "still wished"
+ nbtestsok=`expr $nbtestsok + 1`
+ else
+ echo "Good news! (wish seems to be granted, please check)"
+ fi
+ done
+}
+
# Programme principal
echo "Success tests"
test_success success
echo "Failure tests"
test_failure failure
+echo "Bugs tests"
+test_bugs bugs
echo "Output tests"
test_output output
echo "Parser tests"
test_parser parser
echo "Interactive tests"
test_interactive interactive
+echo "Micromega tests"
+test_success micromega
echo "Complexity tests"
test_complexity complexity
echo "Module tests"
$coqtop -compile modules/Nat
$coqtop -compile modules/plik
test_success modules "-I modules -impredicative-set"
+#echo "Ideal-features tests"
+#test_features ideal-features
pourcentage=`expr 100 \* $nbtestsok / $nbtests`
echo
echo "$nbtestsok tests passed over $nbtests, i.e. $pourcentage %"
-
-#echo "Ideal-features tests"
-#test_success ideal-features
diff --git a/test-suite/complexity/injection.v b/test-suite/complexity/injection.v
new file mode 100644
index 00000000..eb01133e
--- /dev/null
+++ b/test-suite/complexity/injection.v
@@ -0,0 +1,113 @@
+(* This example, submitted by A. Appel, checks the efficiency of
+ injection (see bug #1173) *)
+(* Expected time < 1.50s *)
+
+Set Implicit Arguments.
+
+Record joinable (t: Type) : Type := Joinable {
+ is_empty: t -> Prop;
+ join: t -> t -> t -> Prop;
+ join_com: forall a b c, join a b c -> join b a c;
+ join_empty: forall e a b, is_empty e -> join e a b -> a=b;
+ exists_empty: forall a, exists e, is_empty e /\ join e a a;
+ join_empty2: forall a b c, join a b c -> is_empty c -> is_empty a;
+ join_empty3: forall e a, join e a a -> is_empty e;
+ join_assoc: forall a b c d e, join a b d -> join d c e ->
+ exists f, join b c f /\ join a f e;
+ join_eq: forall x y z z', join x y z -> join x y z' -> z = z';
+ cancellation: forall a1 a2 b c, join a1 b c -> join a2 b c -> a1=a2
+}.
+
+Record joinmap (key: Type) (t: Type) (j : joinable t) : Type
+ := Joinmap {
+ jm_t : Type;
+ jm_j : joinable jm_t;
+ lookup: jm_t -> key -> t;
+ prim : forall (f: key -> t) (e: t),
+ (forall k, j.(join) e (f k) (f k)) ->
+ jm_t;
+ join_rule: forall s1 s2 s,
+ jm_j.(join) s1 s2 s <->
+ forall x, j.(join) (lookup s1 x) (lookup s2 x) (lookup s x);
+ empty_rule: forall e x, jm_j.(is_empty) e -> j.(is_empty) (lookup e x);
+ prim_rule: forall f e pf k, lookup (prim f e pf) k = f k;
+ ext: forall s1 s2,
+ (forall x, lookup s1 x = lookup s2 x) <-> s1 = s2;
+ can_join: forall s1 s2,
+ (forall x, exists v,
+ j.(join) (lookup s1 x) (lookup s2 x) v) ->
+ exists s3, jm_j.(join) s1 s2 s3;
+ can_split: forall s1 s3,
+ (forall x, exists v,
+ j.(join) (lookup s1 x) v (lookup s3 x)) ->
+ exists s2, jm_j.(join) s1 s2 s3
+}.
+
+Parameter mkJoinmap : forall (key: Type) (t: Type) (j: joinable t),
+joinmap key j.
+
+Parameter ADMIT: forall p: Prop, p.
+Implicit Arguments ADMIT [p].
+
+Module Share.
+Parameter jb : joinable bool.
+Definition jm: joinmap nat jb := mkJoinmap nat jb.
+Definition t := jm.(jm_t).
+Definition j := jm.(jm_j).
+Parameter nonempty: t -> Prop.
+End Share.
+
+Section Own.
+
+Variable inv : Type.
+
+Inductive own : Type :=
+ | NO
+ | VAL' : forall sh, Share.nonempty sh -> own
+ | LK : forall sh, Share.nonempty sh -> Share.t -> inv -> own
+ | CT : forall sh, Share.nonempty sh -> own
+ | FUN: forall sh, Share.nonempty sh -> inv -> own.
+
+Definition own_join (a b c: own) : Prop :=
+ match a , b , c with
+ | NO , _ , _ => b=c
+ | _ , NO , _ => a=c
+ | VAL' sa _ , VAL' sb _, VAL' sc _ => Share.j.(join) sa sb sc
+ | LK sa pa ha fa, LK sb pb hb fb, LK sc pc hc fc =>
+ Share.j.(join) sa sb sc /\
+ Share.j.(join) ha hb hc /\
+ fa=fc /\
+ fb=fc
+ | CT sa pa , CT sb pb, CT sc pc => Share.j.(join) sa sb sc
+ | FUN sa pa fa, FUN sb pb fb, FUN sc pc fc =>
+ Share.j.(join) sa sb sc /\ fa=fc /\ fb=fc
+ | _ , _ , _ => False
+ end.
+
+Definition own_is_empty (a: own) := a=NO.
+
+Definition jown : joinable own :=
+ Joinable own_is_empty own_join
+ ADMIT ADMIT ADMIT ADMIT ADMIT ADMIT ADMIT ADMIT .
+End Own.
+
+Fixpoint sinv (n: nat) : Type :=
+ match n with
+ | O => unit
+ | S n => prodT (sinv n) (own (sinv n) -> unit -> Prop)
+ end.
+
+Parameter address: Set.
+
+Definition jm (n: nat) := mkJoinmap address (jown (sinv n)).
+
+Definition worldfun (n: nat) := (jm n).(jm_t).
+
+Inductive world : Type :=
+ mk_world: forall n, worldfun n -> world.
+
+Lemma test: forall n1 w1 n2 w2, mk_world n1 w1 = mk_world n2 w2 ->
+ n1 = n2.
+Proof.
+intros.
+Time injection H.
diff --git a/test-suite/complexity/ring.v b/test-suite/complexity/ring.v
new file mode 100644
index 00000000..5a541bc2
--- /dev/null
+++ b/test-suite/complexity/ring.v
@@ -0,0 +1,7 @@
+(* This example, checks the efficiency of the abstract machine used by ring *)
+(* Expected time < 1.00s *)
+
+Require Import ZArith.
+Open Scope Z_scope.
+Goal forall a, a+a+a+a+a+a+a+a+a+a+a+a+a = a*13.
+Time intro; ring.
diff --git a/test-suite/complexity/ring2.v b/test-suite/complexity/ring2.v
new file mode 100644
index 00000000..9f9685dd
--- /dev/null
+++ b/test-suite/complexity/ring2.v
@@ -0,0 +1,51 @@
+(* This example, checks the efficiency of the abstract machine used by ring *)
+(* Expected time < 1.00s *)
+
+Require Import BinInt.
+
+Definition Zplus x y :=
+match x with
+| 0%Z => y
+| Zpos x' =>
+ match y with
+ | 0%Z => x
+ | Zpos y' => Zpos (x' + y')
+ | Zneg y' =>
+ match (x' ?= y')%positive Eq with
+ | Eq => 0%Z
+ | Lt => Zneg (y' - x')
+ | Gt => Zpos (x' - y')
+ end
+ end
+| Zneg x' =>
+ match y with
+ | 0%Z => x
+ | Zpos y' =>
+ match (x' ?= y')%positive Eq with
+ | Eq => 0%Z
+ | Lt => Zpos (y' - x')
+ | Gt => Zneg (x' - y')
+ end
+ | Zneg y' => Zneg (x' + y')
+ end
+end.
+
+Require Import Ring.
+
+Lemma Zth : ring_theory Z0 (Zpos xH) Zplus Zmult Zminus Zopp (@eq Z).
+Admitted.
+
+Ltac Zcst t :=
+ match isZcst t with
+ true => t
+ | _ => constr:NotConstant
+ end.
+
+Add Ring Zr : Zth
+ (decidable Zeqb_ok, constants [Zcst]).
+
+Open Scope Z_scope.
+Infix "+" := Zplus : Z_scope.
+
+Goal forall a, a+a+a+a+a+a+a+a+a+a+a+a+a = a*13.
+Time intro; ring.
diff --git a/test-suite/csdp.cache b/test-suite/csdp.cache
new file mode 100644
index 00000000..59ff450c
--- /dev/null
+++ b/test-suite/csdp.cache
@@ -0,0 +1,106548 @@
+*** REQUEST ***
+""
+3
+3
+4 1 1
+0.10485760000000000000e7 -0.52428800000000000000e6 0.52428800000000000000e6
+0 1 1 2 -0.52428800000000000000e6
+0 1 1 4 0.52428800000000000000e6
+0 1 2 2 -0.10485760000000000000e7
+0 1 4 4 0.10485760000000000000e7
+0 2 1 1 -0.10485760000000000000e7
+1 1 1 1 0.10485760000000000000e7
+1 1 1 2 0.52428800000000000000e6
+1 1 1 4 -0.52428800000000000000e6
+1 1 2 2 0.10485760000000000000e7
+1 1 4 4 -0.10485760000000000000e7
+1 2 1 1 0.10485760000000000000e7
+2 1 1 3 0.10485760000000000000e7
+2 1 1 4 -0.52428800000000000000e6
+2 1 4 4 -0.10485760000000000000e7
+3 1 1 2 -0.52428800000000000000e6
+3 1 1 4 0.52428800000000000000e6
+3 3 1 1 0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+8
+4
+4 1 4 1
+-0.52428800000000000000e6 0.10485760000000000000e7 -0.52428800000000000000e6 0.0 -0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.10485760000000000000e7
+0 1 1 2 -0.26214400000000000000e6
+0 1 1 4 0.26214400000000000000e6
+0 2 1 1 -0.52428800000000000000e6
+0 3 1 2 -0.26214400000000000000e6
+0 3 1 4 -0.26214400000000000000e6
+1 1 2 3 0.52428800000000000000e6
+1 1 3 4 -0.52428800000000000000e6
+1 3 1 4 -0.26214400000000000000e6
+1 3 4 4 -0.52428800000000000000e6
+2 1 1 1 0.52428800000000000000e6
+2 1 1 2 0.26214400000000000000e6
+2 1 1 4 -0.26214400000000000000e6
+2 2 1 1 0.52428800000000000000e6
+2 3 1 2 0.26214400000000000000e6
+2 3 1 4 0.26214400000000000000e6
+3 1 1 3 0.52428800000000000000e6
+3 1 1 4 -0.26214400000000000000e6
+3 1 4 4 -0.52428800000000000000e6
+4 1 2 2 0.52428800000000000000e6
+4 1 4 4 -0.52428800000000000000e6
+4 3 1 2 -0.26214400000000000000e6
+4 3 1 4 -0.26214400000000000000e6
+5 1 2 4 0.52428800000000000000e6
+5 1 4 4 -0.10485760000000000000e7
+5 3 1 4 -0.52428800000000000000e6
+6 1 1 2 -0.26214400000000000000e6
+6 1 1 4 0.26214400000000000000e6
+6 3 1 1 0.52428800000000000000e6
+7 1 2 3 -0.52428800000000000000e6
+7 1 3 4 0.52428800000000000000e6
+7 3 1 3 0.52428800000000000000e6
+8 1 1 2 0.26214400000000000000e6
+8 1 1 4 -0.26214400000000000000e6
+8 1 2 3 -0.52428800000000000000e6
+8 1 3 4 0.52428800000000000000e6
+8 3 1 2 0.26214400000000000000e6
+8 3 2 2 0.52428800000000000000e6
+8 4 1 1 0.52428800000000000000e6
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+51
+4
+10 4 4 1
+0.52428800000000000000e6 0.0 0.0 -0.52428800000000000000e6 0.0 0.0 0.0 0.0 0.0 0.0 0.10485760000000000000e7 0.0 0.0 -0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.0 0.0 0.0 0.10485760000000000000e7 0.0 0.0 0.0 0.0 0.52428800000000000000e6 -0.52428800000000000000e6 0.0 0.0 0.0 0.52428800000000000000e6 0.0 0.0 0.0 -0.10485760000000000000e7 0.10485760000000000000e7 0.0 0.52428800000000000000e6 0.0 0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.0 -0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.0 0.52428800000000000000e6 0.52428800000000000000e6
+0 1 1 2 -0.13107200000000000000e6
+0 1 1 4 0.26214400000000000000e6
+0 1 1 8 -0.13107200000000000000e6
+0 2 1 1 -0.26214400000000000000e6
+0 3 1 2 -0.13107200000000000000e6
+1 1 2 9 -0.26214400000000000000e6
+1 1 7 10 0.13107200000000000000e6
+1 1 10 10 0.26214400000000000000e6
+1 3 3 4 0.26214400000000000000e6
+2 1 2 9 0.13107200000000000000e6
+2 1 6 7 -0.26214400000000000000e6
+2 1 9 10 0.13107200000000000000e6
+2 3 3 4 -0.13107200000000000000e6
+3 1 2 9 -0.26214400000000000000e6
+3 1 7 8 0.13107200000000000000e6
+3 1 8 10 0.13107200000000000000e6
+4 1 2 9 0.26214400000000000000e6
+4 1 3 10 -0.13107200000000000000e6
+4 1 4 7 -0.26214400000000000000e6
+4 1 7 8 -0.13107200000000000000e6
+4 1 7 10 0.13107200000000000000e6
+4 2 4 4 -0.26214400000000000000e6
+4 3 3 4 -0.26214400000000000000e6
+5 1 1 6 -0.13107200000000000000e6
+5 1 3 6 -0.13107200000000000000e6
+5 1 4 5 -0.13107200000000000000e6
+5 1 6 7 0.13107200000000000000e6
+5 1 9 9 0.26214400000000000000e6
+5 2 3 3 -0.26214400000000000000e6
+6 1 2 9 0.13107200000000000000e6
+6 1 4 5 -0.26214400000000000000e6
+6 1 8 9 0.13107200000000000000e6
+7 1 1 6 -0.26214400000000000000e6
+7 1 2 9 0.13107200000000000000e6
+7 1 4 7 0.13107200000000000000e6
+7 3 3 4 -0.13107200000000000000e6
+8 1 1 8 -0.13107200000000000000e6
+8 1 2 5 -0.26214400000000000000e6
+8 1 2 9 0.26214400000000000000e6
+8 1 3 8 -0.13107200000000000000e6
+8 1 3 10 0.13107200000000000000e6
+8 2 2 4 -0.13107200000000000000e6
+9 1 1 4 0.26214400000000000000e6
+9 1 1 6 -0.52428800000000000000e6
+9 1 1 8 0.13107200000000000000e6
+9 1 2 5 0.26214400000000000000e6
+9 1 7 8 0.13107200000000000000e6
+9 2 1 3 0.26214400000000000000e6
+10 1 1 2 0.13107200000000000000e6
+10 1 1 6 -0.52428800000000000000e6
+10 1 1 8 0.13107200000000000000e6
+10 1 2 3 0.13107200000000000000e6
+10 1 2 5 0.26214400000000000000e6
+10 1 3 8 0.13107200000000000000e6
+10 1 3 10 -0.13107200000000000000e6
+10 1 4 7 0.26214400000000000000e6
+10 1 7 8 -0.13107200000000000000e6
+10 2 1 3 0.26214400000000000000e6
+10 2 2 4 0.13107200000000000000e6
+10 2 4 4 -0.26214400000000000000e6
+10 3 1 2 0.13107200000000000000e6
+10 3 3 4 -0.26214400000000000000e6
+10 4 1 1 0.26214400000000000000e6
+11 1 1 1 0.26214400000000000000e6
+11 1 1 2 0.13107200000000000000e6
+11 1 1 4 -0.26214400000000000000e6
+11 1 1 8 0.13107200000000000000e6
+11 2 1 1 0.26214400000000000000e6
+11 3 1 2 0.13107200000000000000e6
+12 1 1 3 0.26214400000000000000e6
+12 1 1 8 -0.26214400000000000000e6
+12 3 1 2 -0.26214400000000000000e6
+13 1 1 4 0.26214400000000000000e6
+13 1 1 5 0.26214400000000000000e6
+13 1 1 6 -0.52428800000000000000e6
+13 1 2 5 0.26214400000000000000e6
+13 2 1 3 0.26214400000000000000e6
+14 1 1 2 -0.26214400000000000000e6
+14 1 1 4 -0.52428800000000000000e6
+14 1 1 6 0.10485760000000000000e7
+14 1 1 7 0.26214400000000000000e6
+14 1 1 8 -0.26214400000000000000e6
+14 1 2 3 -0.26214400000000000000e6
+14 1 2 5 -0.52428800000000000000e6
+14 1 2 9 0.52428800000000000000e6
+14 1 3 8 -0.26214400000000000000e6
+14 1 4 7 -0.52428800000000000000e6
+14 2 1 3 -0.52428800000000000000e6
+14 2 2 4 -0.26214400000000000000e6
+14 3 1 2 -0.26214400000000000000e6
+14 4 1 1 -0.52428800000000000000e6
+15 1 1 9 0.26214400000000000000e6
+15 1 4 7 -0.26214400000000000000e6
+16 1 1 10 0.26214400000000000000e6
+16 1 2 9 -0.52428800000000000000e6
+16 1 3 10 0.26214400000000000000e6
+16 1 7 8 0.26214400000000000000e6
+16 2 4 4 0.52428800000000000000e6
+16 3 3 4 0.52428800000000000000e6
+17 1 1 8 -0.13107200000000000000e6
+17 1 2 2 0.26214400000000000000e6
+17 3 1 2 -0.13107200000000000000e6
+18 1 1 4 0.26214400000000000000e6
+18 1 1 6 -0.52428800000000000000e6
+18 1 2 4 0.26214400000000000000e6
+18 1 2 5 0.26214400000000000000e6
+18 2 1 3 0.26214400000000000000e6
+19 1 2 6 0.26214400000000000000e6
+19 1 4 5 -0.26214400000000000000e6
+20 1 1 8 -0.26214400000000000000e6
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+21 1 1 8 0.26214400000000000000e6
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+21 1 2 9 -0.52428800000000000000e6
+21 1 3 8 0.26214400000000000000e6
+21 2 2 4 0.26214400000000000000e6
+22 1 2 10 0.26214400000000000000e6
+22 1 7 8 -0.26214400000000000000e6
+23 1 1 8 0.13107200000000000000e6
+23 1 2 3 0.13107200000000000000e6
+23 1 2 5 -0.26214400000000000000e6
+23 1 3 3 0.26214400000000000000e6
+23 2 2 2 0.26214400000000000000e6
+23 3 1 2 0.13107200000000000000e6
+24 1 2 5 -0.26214400000000000000e6
+24 1 3 4 0.26214400000000000000e6
+25 1 1 4 -0.26214400000000000000e6
+25 1 1 6 0.52428800000000000000e6
+25 1 3 5 0.26214400000000000000e6
+25 1 4 5 -0.52428800000000000000e6
+25 2 1 3 -0.26214400000000000000e6
+25 2 2 3 0.26214400000000000000e6
+26 1 1 8 0.26214400000000000000e6
+26 1 2 9 -0.52428800000000000000e6
+26 1 3 7 0.26214400000000000000e6
+26 1 3 8 0.26214400000000000000e6
+26 2 2 4 0.26214400000000000000e6
+27 1 3 9 0.26214400000000000000e6
+27 1 5 8 -0.26214400000000000000e6
+28 1 1 6 -0.13107200000000000000e6
+28 1 4 4 0.26214400000000000000e6
+29 1 1 6 -0.13107200000000000000e6
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+29 1 4 5 -0.13107200000000000000e6
+29 1 4 6 0.26214400000000000000e6
+29 2 3 3 -0.26214400000000000000e6
+30 1 2 9 -0.26214400000000000000e6
+30 1 4 8 0.26214400000000000000e6
+31 1 4 9 0.26214400000000000000e6
+31 1 6 7 -0.26214400000000000000e6
+32 1 2 9 -0.26214400000000000000e6
+32 1 4 10 0.26214400000000000000e6
+32 3 3 4 0.26214400000000000000e6
+33 1 3 6 -0.13107200000000000000e6
+33 1 5 5 0.26214400000000000000e6
+34 1 2 9 -0.26214400000000000000e6
+34 1 5 7 0.26214400000000000000e6
+35 1 5 10 0.26214400000000000000e6
+35 1 8 9 -0.26214400000000000000e6
+36 1 5 9 -0.26214400000000000000e6
+36 1 6 8 0.26214400000000000000e6
+37 1 6 10 0.26214400000000000000e6
+37 1 9 9 -0.52428800000000000000e6
+38 1 2 9 -0.26214400000000000000e6
+38 1 3 10 0.13107200000000000000e6
+38 1 7 7 0.26214400000000000000e6
+38 1 7 8 0.13107200000000000000e6
+38 2 4 4 0.26214400000000000000e6
+38 3 3 4 0.26214400000000000000e6
+39 1 2 9 -0.26214400000000000000e6
+39 1 7 9 0.26214400000000000000e6
+39 3 3 4 0.26214400000000000000e6
+40 1 3 10 -0.13107200000000000000e6
+40 1 8 8 0.26214400000000000000e6
+41 1 1 2 0.26214400000000000000e6
+41 1 1 4 0.52428800000000000000e6
+41 1 1 6 -0.10485760000000000000e7
+41 1 1 8 0.26214400000000000000e6
+41 1 2 3 0.26214400000000000000e6
+41 1 2 5 0.52428800000000000000e6
+41 2 1 2 0.26214400000000000000e6
+41 2 1 3 0.52428800000000000000e6
+41 3 1 2 0.26214400000000000000e6
+42 1 1 2 0.26214400000000000000e6
+42 1 1 4 0.52428800000000000000e6
+42 1 1 6 -0.10485760000000000000e7
+42 1 1 8 0.26214400000000000000e6
+42 1 2 3 0.26214400000000000000e6
+42 1 2 5 0.52428800000000000000e6
+42 2 1 3 0.52428800000000000000e6
+42 2 1 4 0.26214400000000000000e6
+42 3 1 2 0.26214400000000000000e6
+42 4 1 1 0.52428800000000000000e6
+43 1 2 9 0.26214400000000000000e6
+43 1 4 7 0.26214400000000000000e6
+43 1 5 8 0.26214400000000000000e6
+43 1 6 7 -0.52428800000000000000e6
+43 2 3 4 0.26214400000000000000e6
+44 1 1 4 0.26214400000000000000e6
+44 1 1 6 -0.52428800000000000000e6
+44 1 1 8 0.13107200000000000000e6
+44 1 2 3 0.13107200000000000000e6
+44 1 2 5 0.26214400000000000000e6
+44 1 2 9 -0.26214400000000000000e6
+44 1 3 8 0.13107200000000000000e6
+44 1 4 7 0.26214400000000000000e6
+44 2 1 3 0.26214400000000000000e6
+44 2 2 4 0.13107200000000000000e6
+44 3 1 1 0.26214400000000000000e6
+44 3 1 2 0.13107200000000000000e6
+44 4 1 1 0.26214400000000000000e6
+45 1 1 4 0.26214400000000000000e6
+45 1 1 6 -0.52428800000000000000e6
+45 1 2 5 0.26214400000000000000e6
+45 1 4 7 0.26214400000000000000e6
+45 2 1 3 0.26214400000000000000e6
+45 3 1 3 0.26214400000000000000e6
+46 1 1 8 -0.26214400000000000000e6
+46 1 2 9 0.52428800000000000000e6
+46 1 3 10 -0.26214400000000000000e6
+46 1 7 8 -0.26214400000000000000e6
+46 2 4 4 -0.52428800000000000000e6
+46 3 1 4 0.26214400000000000000e6
+46 3 3 4 -0.52428800000000000000e6
+47 1 1 8 -0.13107200000000000000e6
+47 1 2 3 -0.13107200000000000000e6
+47 1 2 9 0.26214400000000000000e6
+47 1 3 8 -0.13107200000000000000e6
+47 2 2 4 -0.13107200000000000000e6
+47 3 2 2 0.26214400000000000000e6
+48 1 2 5 -0.26214400000000000000e6
+48 1 2 9 0.26214400000000000000e6
+48 3 2 3 0.26214400000000000000e6
+49 1 1 8 0.26214400000000000000e6
+49 1 2 9 -0.52428800000000000000e6
+49 1 3 8 0.26214400000000000000e6
+49 1 7 8 0.26214400000000000000e6
+49 2 2 4 0.26214400000000000000e6
+49 3 2 4 0.26214400000000000000e6
+50 1 4 5 -0.13107200000000000000e6
+50 1 6 7 0.13107200000000000000e6
+50 3 3 3 0.26214400000000000000e6
+51 1 7 8 -0.13107200000000000000e6
+51 1 7 10 0.13107200000000000000e6
+51 3 4 4 0.26214400000000000000e6
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+96
+4
+10 4 10 4
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+281
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+468
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+1582
+4
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+4310
+4
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+*** ANSWER ***
+Failure
+*** END ***
+*** REQUEST ***
+""
+1
+3
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+Failure
+*** END ***
+*** REQUEST ***
+""
+20
+7
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+20 7 1 1 0.52428800000000000000e6
+*** ANSWER ***
+1.408782095084682300e-09 -1.602914970239133998e-09 -2.114475512891011934e-10 1.060506402935637712e-09 2.087517807687731792e-10 1.077350266300643788e+00 2.270314862475966567e-09 3.943375646635861598e-01 1.443375636846786492e-01 -1.043524690896394265e-09 1.443375641664579045e-01 7.735026962533857187e-02 -1.056624334368447687e-01 -6.083345939969603797e-10 1.443375650931136012e-01 8.310024134167537971e-10 1.443375652667332198e-01 8.309942911694060400e-10 6.728192240935055053e-11 -1.043513922667392298e-09
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+*** END ***
+*** REQUEST ***
+""
+5
+5
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+*** ANSWER ***
+Failure
+*** END ***
+*** REQUEST ***
+""
+20
+7
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+*** ANSWER ***
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+*** REQUEST ***
+""
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
+4
+5
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+4 5 1 1 0.52428800000000000000e6
+*** ANSWER ***
+-2.874631848909842333e-09 8.664272116492426616e-24 -8.301572844558803433e-10 9.999999947692463920e-01
+1 1 1 1 2.934653518525875623e-04
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+*** END ***
+*** REQUEST ***
+""
+1
+2
+3 1
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+1 2 1 1 -0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+4
+3
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+*** ANSWER ***
+Failure
+*** END ***
+*** REQUEST ***
+""
+14
+4
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+14 3 3 3 0.52428800000000000000e6
+*** ANSWER ***
+-1.106847476088164140e-10 7.356791287437961024e-11 1.626260578934070067e-09 8.464732015420119625e-10 8.464732012511223196e-10 1.449010447439587610e-09 1.921197997299696732e-09 1.941780561617547037e-09 6.562099206323578718e-10 3.681286449449734143e-09 9.801835322020321617e-10 -8.499142509722558133e-10 9.999999988286795150e-01 9.999999988286794039e-01
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+2 4 1 1 9.351632690430405903e-01
+*** END ***
+*** REQUEST ***
+""
+68
+13
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+68 1 4 5 -0.26214400000000000000e6
+68 1 5 6 0.26214400000000000000e6
+68 13 1 1 0.52428800000000000000e6
+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
+1
+5
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+1 1 1 1 0.10485760000000000000e7
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+1 4 1 1 0.52428800000000000000e6
+*** ANSWER ***
+5.000000009006688728e-01
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+2 5 1 1 1.434681423197123440e+00
+*** END ***
+*** REQUEST ***
+""
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
+47
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
+1
+6
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+1 1 1 1 0.10485760000000000000e7
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+1 4 1 1 0.52428800000000000000e6
+*** ANSWER ***
+5.000000006889400161e-01
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+2 5 1 1 4.901085593439381327e+00
+2 6 1 1 4.901085593439381327e+00
+*** END ***
+*** REQUEST ***
+""
+57
+16
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
+47
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
+47
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+2.499997645979282479e-01 2.500002357495276217e-01
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+6.390535959450866983e-11 -7.081165828606712792e-11 9.999999998131693379e-01 9.999999999222820568e-01
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+6.390682943459618358e-11 -7.081294109863518471e-11 9.999999998131664514e-01 9.999999999222810576e-01
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+2.417243834881730172e-10 -9.999999997582740274e-01 -2.417249248510537096e-10 -6.516102507854656631e-31 1.082378559825435644e-15
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+2.417243834881730172e-10 9.999999997582740274e-01 -2.417249248510537096e-10 6.516102507854656631e-31 1.082378559825435644e-15
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+*** END ***
+*** REQUEST ***
+""
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+7 1 3 3 0.10485760000000000000e7
+*** ANSWER ***
+-6.610729450860498568e-01 -3.389270548050536402e-01 1.088966114251059482e-10 0.000000000000000000e+00 -1.088966114252581494e-10 0.000000000000000000e+00 -1.088966114251092569e-10
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+2 1 2 3 4.987329993433329641e-18
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+2 2 1 1 1.440533100777350242e-22
+*** END ***
+*** REQUEST ***
+""
+7
+2
+3 1
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+*** ANSWER ***
+6.610729450860498568e-01 3.389270548050536402e-01 1.088966114251059482e-10 0.000000000000000000e+00 -1.088966114252581494e-10 0.000000000000000000e+00 -1.088966114251092569e-10
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+2 1 2 3 -4.987329993433329641e-18
+2 1 3 3 5.000000000000000000e-01
+2 2 1 1 1.440533100777350242e-22
+*** END ***
+*** REQUEST ***
+""
+5
+3
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+-0.52428800000000000000e6 0.0 0.10485760000000000000e7 0.0 0.0
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+*** ANSWER ***
+2.417243834881730172e-10 -9.999999997582740274e-01 -2.417249248510537096e-10 6.516102507854656631e-31 1.082378559825435644e-15
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+2 2 1 1 5.413640376397729861e-16
+2 3 1 1 1.646717611279745635e-06
+*** END ***
+*** REQUEST ***
+""
+5
+3
+3 1 1
+-0.52428800000000000000e6 0.0 0.10485760000000000000e7 0.0 0.0
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+*** ANSWER ***
+2.417243834881730172e-10 9.999999997582740274e-01 -2.417249248510537096e-10 -6.516102507854656631e-31 1.082378559825435644e-15
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+2 3 1 1 1.646717611279745635e-06
+*** END ***
+*** REQUEST ***
+""
+4
+5
+3 1 1 1 1
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+*** ANSWER ***
+6.390550264518323903e-11 7.081185573184761103e-11 9.999999998131687828e-01 9.999999999222817237e-01
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+2 5 1 1 1.798328611025971288e-10
+*** END ***
+*** REQUEST ***
+""
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+3 1 1
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+*** ANSWER ***
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+2 2 1 1 3.315809821104277243e-16
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+*** END ***
+*** REQUEST ***
+""
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+3
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+*** ANSWER ***
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+2 2 1 1 3.315809821104277243e-16
+2 3 1 1 8.049700105932944581e-07
+*** END ***
+*** REQUEST ***
+""
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+5
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+*** ANSWER ***
+6.390905338787261955e-11 7.081709479863854861e-11 9.999999998131536838e-01 9.999999999222748404e-01
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+-3.988166713257686148e-10 -1.023140901531525444e-11 2.046281803062761375e-11 9.999999988992015476e-01
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+*** END ***
+*** REQUEST ***
+""
+1
+1
+2
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+*** ANSWER ***
+-1.257428932280705548e-10
+1 1 1 1 4.067801944678135183e-18
+1 1 2 2 1.048576000000000000e+06
+2 1 1 1 1.000000000000000000e+00
+2 1 2 2 8.401557020587951909e-24
+*** END ***
+*** REQUEST ***
+""
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+2
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+*** ANSWER ***
+3.613357717503612232e+00 2.020964573331731629e+00
+1 1 1 1 2.841660136565609369e+06
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+2 2 1 1 1.154826371740193283e-08
+*** END ***
+*** REQUEST ***
+""
+6
+5
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
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+*** END ***
+*** REQUEST ***
+""
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+*** REQUEST ***
+""
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+*** ANSWER ***
+3.333333330362959201e-01
+1 1 1 1 4.314859080885419772e-04
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+2 3 1 1 6.573647156062306478e-15
+2 4 1 1 2.755646794823147941e-15
+*** END ***
+*** REQUEST ***
+""
+2
+5
+1 1 1 1 1
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+2 5 1 1 0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+14
+15
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+14 15 1 1 0.52428800000000000000e6
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+50
+35
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+50 35 1 1 0.26214400000000000000e6
+*** ANSWER ***
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+2 34 1 1 5.034119478263683334e-01
+2 35 1 1 4.724555662851357973e-01
+*** END ***
+*** REQUEST ***
+""
+1
+5
+1 1 1 1 1
+0.10485760000000000000e7
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+1 5 1 1 0.52428800000000000000e6
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+10
+11
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+41
+16
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+41 15 1 1 0.13107200000000000000e6
+*** ANSWER ***
+-2.796428333061710846e-10 -5.145505709403082136e-12 -5.145505710399421184e-12 -5.065723613441632291e-11 5.112487019279347381e-11 5.112487019517472000e-11 -5.065723614645774618e-11 5.112487019298682728e-11 -5.065723613233761803e-11 -3.227934490141472682e-10 -2.726207292780503898e-11 8.167675251916435826e-11 3.251989134141424605e-10 8.167675250840997632e-11 8.167675251988690053e-11 -1.518635855095441632e-10 1.133140151751466980e-11 1.133166704855965140e-11 1.464637579379667940e-11 1.464320231899948338e-11 -3.333333329650279842e-01 -5.483000373986155436e-11 1.133261561376234559e-11 1.133045304810582364e-11 3.333333328223528347e-01 1.464445376592864346e-11 -3.333333329650249865e-01 1.464512448280788691e-11 3.333333328223558323e-01 -5.483000374452421638e-11 3.333333321195710020e-01 1.556001119344247636e-11 1.133310736505450625e-11 -1.518635855118056750e-10 -3.333333329650288168e-01 1.464347951112338470e-11 1.464609861685960086e-11 -5.483000373986801671e-11 3.333333321195705023e-01 7.578414394855302048e-11 3.333333321195734444e-01
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+2 15 1 1 1.396360650674362019e-09
+2 16 1 1 3.483236495771939722e+00
+*** END ***
+*** REQUEST ***
+""
+2
+2
+4 1
+-0.26214400000000000000e6 -0.13107200000000000000e7
+0 1 2 2 0.52428800000000000000e6
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+2 1 3 4 0.52428800000000000000e6
+2 1 4 4 -0.15728640000000000000e7
+2 2 1 1 -0.52428800000000000000e6
+*** ANSWER ***
+-1.369805830780025199e-10 -9.999999997258860462e-01
+1 1 1 1 4.004402490975419925e-07
+1 1 2 2 1.048575999712891062e+06
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+2 1 2 2 8.333333333287741285e-01
+2 1 2 3 8.333333333282649802e-01
+2 1 2 4 8.333333333328124537e-01
+2 1 3 3 8.333333333287741285e-01
+2 1 3 4 8.333333333328124537e-01
+2 1 4 4 8.333333333378689645e-01
+2 2 1 1 1.527559509425708661e-12
+*** END ***
+*** REQUEST ***
+""
+2
+2
+5 1
+-0.19660800000000000000e6 -0.11141120000000000000e7
+0 1 2 2 0.26214400000000000000e6
+0 1 3 3 0.26214400000000000000e6
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+2 1 4 5 0.26214400000000000000e6
+2 1 5 5 -0.10485760000000000000e7
+2 2 1 1 -0.26214400000000000000e6
+*** ANSWER ***
+-2.348240940930787258e-09 -9.999999946942671469e-01
+1 1 1 1 9.050318275803589940e-04
+1 1 2 2 7.864319965727222152e+05
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+1 1 3 5 -2.621439986091339670e+05
+1 1 4 4 7.864319965727222152e+05
+1 1 4 5 -2.621439986091339670e+05
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+1 2 1 1 2.621440001297430717e+05
+2 1 1 1 3.499999985499439692e+00
+2 1 2 2 1.062499996374859812e+00
+2 1 2 3 1.062499995468575209e+00
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+2 1 2 5 1.062499995468574987e+00
+2 1 3 3 1.062499996374860034e+00
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+2 1 4 5 1.062499995468574987e+00
+2 1 5 5 1.062499996374859368e+00
+2 2 1 1 3.625141883504653676e-09
+*** END ***
+*** REQUEST ***
+""
+4
+5
+3 1 1 1 1
+0.52428800000000000000e6 -0.10485760000000000000e7 0.52428800000000000000e6 0.10485760000000000000e7
+0 1 1 2 0.13107200000000000000e6
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+4 1 2 3 -0.13107200000000000000e6
+4 4 1 1 0.26214400000000000000e6
+4 5 1 1 0.26214400000000000000e6
+*** ANSWER ***
+4.548904692939137619e-10 -1.674174344389079182e-09 9.029409809493680191e-10 9.999999937581930398e-01
+1 1 1 1 6.148414788495325939e-04
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+2 1 1 1 5.999999993617382010e+00
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+2 2 1 1 3.191312840597110303e-09
+2 3 1 1 1.534311098449921529e+00
+2 4 1 1 1.534311099393473210e+00
+2 5 1 1 3.191307237696616244e-09
+*** END ***
+*** REQUEST ***
+""
+4
+5
+3 1 1 1 1
+0.52428800000000000000e6 -0.10485760000000000000e7 0.52428800000000000000e6 0.15728640000000000000e7
+0 1 1 2 -0.13107200000000000000e6
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+4 1 2 3 -0.13107200000000000000e6
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+4 5 1 1 0.26214400000000000000e6
+*** ANSWER ***
+9.046097392403201396e-10 -4.087614502059694096e-10 9.999999977383847716e-01 9.999999965640337107e-01
+1 1 1 1 3.604559925710001944e-04
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+2 1 1 1 9.999999991249831410e+00
+2 1 1 2 1.399999998468725870e+01
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+2 2 1 1 2.187501854030851450e-09
+2 3 1 1 2.187502197415109826e-09
+2 4 1 1 2.187502197415096591e-09
+2 5 1 1 2.187502181997641114e-09
+*** END ***
+*** REQUEST ***
+""
+3
+7
+1 1 1 1 1 1 1
+0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7
+0 1 1 1 0.10485760000000000000e7
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+2 5 1 1 0.10485760000000000000e7
+3 6 1 1 0.10485760000000000000e7
+3 7 1 1 0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+22
+23
+4 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+0.39321600000000000000e6 0.78643200000000000000e6 -0.14417920000000000000e7 -0.15728640000000000000e7 0.15728640000000000000e7 0.10485760000000000000e7 0.52428800000000000000e6 0.0 0.13107200000000000000e6 0.52428800000000000000e6 0.39321600000000000000e6 0.0 0.52428800000000000000e6 0.52428800000000000000e6 0.0 0.52428800000000000000e6 0.52428800000000000000e6 0.0 0.52428800000000000000e6 0.52428800000000000000e6 0.0 0.14417920000000000000e7
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+22 12 1 1 0.26214400000000000000e6
+22 20 1 1 0.52428800000000000000e6
+22 23 1 1 0.26214400000000000000e6
+*** ANSWER ***
+-1.295667068556624539e-10 -1.626374797343609882e-10 -5.545183488149067688e-10 2.098558964095165409e-11 -5.545183488151598861e-10 2.098558964089881793e-11 -5.151721287085392124e-10 7.692307573534454268e-02 -5.151721287085408668e-10 7.692307481797780455e-02 3.076923070197430388e-01 -5.151707783664954629e-10 7.692307668943522414e-02 -5.151721287085458299e-10 7.692307575370652128e-02 -5.151707783665070434e-10 -5.151707783665070434e-10 3.076923070197430388e-01 -5.151707783665053891e-10 -5.151707783665086978e-10 7.692307575370652128e-02 7.692307573534454268e-02
+1 1 1 1 1.485321445614910807e-04
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+2 22 1 1 4.574427803316027296e-09
+2 23 1 1 4.574428482139586761e-09
+*** END ***
+*** REQUEST ***
+""
+3
+7
+1 1 1 1 1 1 1
+0.0 0.0 0.0
+0 1 1 1 0.52428800000000000000e6
+1 1 1 1 -0.10485760000000000000e7
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+3 1 1 1 -0.10485760000000000000e7
+3 6 1 1 0.52428800000000000000e6
+3 7 1 1 0.52428800000000000000e6
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+22
+23
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+22 4 1 1 0.88473600000000000000e6
+22 8 1 1 -0.13107200000000000000e6
+22 12 1 1 0.65536000000000000000e5
+22 16 1 1 0.32768000000000000000e5
+22 20 1 1 0.13107200000000000000e6
+22 23 1 1 0.65536000000000000000e5
+*** ANSWER ***
+4.049512478004994521e-09 -7.853528065000316224e-10 2.098746827559298714e-09 -1.064002179143037410e-09 2.098746826197792513e-09 -1.064002178236080190e-09 -3.533807468735688266e-10 9.999999893727561373e-01 -3.533807468734935532e-10 -4.066578641307421796e-10 6.106671844491684542e-01 3.473323508561638184e-01 2.694664478268185004e+00 -3.533807468737202007e-10 -4.066578641307620320e-10 3.473327911937711954e-01 3.473340419483763042e-01 6.106687190982799107e-01 3.473330062104405536e-01 3.473326192695437298e-01 2.694666638300601047e+00 9.999999893727561373e-01
+1 1 1 1 2.955311598780135246e-04
+1 1 1 2 -5.146888158159813008e-05
+1 1 1 3 -5.146888152678607241e-05
+1 1 1 4 -5.146888156371399840e-05
+1 1 2 2 1.676857822104013684e-04
+1 1 2 3 -6.973044675111467021e-05
+1 1 2 4 -6.973044681231809969e-05
+1 1 3 3 1.676857821211741317e-04
+1 1 3 4 -6.973044675287975135e-05
+1 1 4 4 1.676857822024493960e-04
+1 2 1 1 6.553599919613178645e+04
+1 3 1 1 6.983149492369882839e-06
+1 4 1 1 4.002087485256239597e+04
+1 5 1 1 6.553599933367525227e+04
+1 6 1 1 6.983149492374788854e-06
+1 7 1 1 3.491580335803661558e-06
+1 8 1 1 2.276275983412596543e+04
+1 9 1 1 4.002068463020300987e+04
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+1 11 1 1 1.765975312779260857e+05
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+1 13 1 1 6.983149492359935285e-06
+1 14 1 1 3.491580335802333410e-06
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+2 8 1 1 1.013005840234281783e-08
+2 9 1 1 5.716805148766916003e-09
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+2 13 1 1 3.399999988197728129e+01
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+2 15 1 1 1.012958682617309905e-08
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+2 21 1 1 1.012966020393385883e-08
+2 22 1 1 1.303327157037172274e-09
+2 23 1 1 3.509889572509255399e-09
+*** END ***
+*** REQUEST ***
+""
+5
+5
+3 1 1 1 1
+0.52428800000000000000e6 -0.10485760000000000000e7 0.10485760000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6
+0 1 2 3 0.26214400000000000000e6
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+4 3 1 1 0.52428800000000000000e6
+5 1 2 3 -0.26214400000000000000e6
+5 5 1 1 0.52428800000000000000e6
+*** ANSWER ***
+9.047144637004025380e-01 -5.064741821662422927e-01 1.012948364956070213e+00 -6.235856335248027958e-10 -5.845221297834649404e-10
+1 1 1 1 4.743309372861008742e+05
+1 1 1 2 -2.655383360195748392e+05
+1 1 1 3 -2.655383360195748392e+05
+1 1 2 2 5.310766729076325428e+05
+1 1 2 3 -2.337711320360052632e+05
+1 1 3 3 5.310766729076325428e+05
+1 2 1 1 5.310766729076325428e+05
+1 3 1 1 2.146057993971965325e-04
+1 4 1 1 2.146057993971661748e-04
+1 5 1 1 2.350863256467333393e-04
+2 1 1 1 4.943559570850903917e+00
+2 1 1 2 4.415339358856920526e+00
+2 1 1 3 4.415339358856921415e+00
+2 1 2 2 3.943559572351147846e+00
+2 1 2 3 3.943559570850906582e+00
+2 1 3 3 3.943559572351153619e+00
+2 2 1 1 2.160644606377368460e-09
+2 3 1 1 5.415339358856919638e+00
+2 4 1 1 5.415339358856934737e+00
+2 5 1 1 4.943559570850906582e+00
+*** END ***
+*** REQUEST ***
+""
+4
+4
+3 1 1 1
+0.0 -0.10485760000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6
+0 4 1 1 0.52428800000000000000e6
+1 1 1 1 0.52428800000000000000e6
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+3 1 1 2 -0.26214400000000000000e6
+3 2 1 1 0.52428800000000000000e6
+4 1 1 3 -0.26214400000000000000e6
+4 3 1 1 0.52428800000000000000e6
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+13
+5
+3 1 3 3 1
+0.0 0.0 0.52428800000000000000e6 -0.10485760000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6 0.52428800000000000000e6 0.0 0.0 0.0 0.52428800000000000000e6 -0.10485760000000000000e7 0.52428800000000000000e6
+0 1 2 3 0.26214400000000000000e6
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+12 4 2 3 0.52428800000000000000e6
+13 1 2 3 -0.26214400000000000000e6
+13 5 1 1 0.52428800000000000000e6
+*** ANSWER ***
+-1.012948329551812909e+00 -1.012948329551812909e+00 9.047145732130862372e-01 -5.064741647124204604e-01 1.012948329986513407e+00 1.012948329986513407e+00 -1.269719777217911070e-10 -2.267145002100386557e-10 1.807584410822154742e-10 -2.267145002104232947e-10 1.807584410826844857e-10 -3.495881670031764897e-10 -2.576717013002858655e-10
+1 1 1 1 4.743309943659727578e+05
+1 1 1 2 -2.655383268687454984e+05
+1 1 1 3 -2.655383268687454984e+05
+1 1 2 2 5.310766542371993419e+05
+1 1 2 3 -2.337711697371662303e+05
+1 1 3 3 5.310766542371993419e+05
+1 2 1 1 5.310766542810912943e+05
+1 3 1 1 1.386602794478742143e-04
+1 3 1 2 2.194599384597073792e-05
+1 3 1 3 -1.188636918861207467e-04
+1 3 2 2 2.052301637036763049e-04
+1 3 2 3 -1.832848809016356280e-04
+1 3 3 3 2.999996452617888915e-04
+1 4 1 1 1.386602794479904407e-04
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+1 4 2 2 2.999996452620360896e-04
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+1 4 3 3 2.052301637036763049e-04
+1 5 1 1 7.013598277235181221e-05
+2 1 1 1 4.943559575736863998e+00
+2 1 1 2 4.415339364265365774e+00
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+2 1 2 2 3.943559576120588606e+00
+2 1 2 3 3.943559575736873768e+00
+2 1 3 3 3.943559576120614807e+00
+2 2 1 1 5.526448483074430500e-10
+2 3 1 1 5.415339364265365774e+00
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+2 3 1 3 3.943559575736864442e+00
+2 3 2 2 5.028789771976822642e+00
+2 3 2 3 4.415339364265383537e+00
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+2 4 1 2 3.943559575736877765e+00
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+2 4 2 2 5.415339364265393307e+00
+2 4 2 3 4.415339364265369326e+00
+2 4 3 3 5.028789771976716061e+00
+2 5 1 1 4.943559575736879985e+00
+*** END ***
+*** REQUEST ***
+""
+3
+4
+3 1 1 1
+-0.10485760000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6
+0 1 1 1 0.52428800000000000000e6
+1 1 2 3 0.52428800000000000000e6
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+2 1 1 2 -0.26214400000000000000e6
+2 2 1 1 0.52428800000000000000e6
+3 1 1 3 -0.26214400000000000000e6
+3 3 1 1 0.52428800000000000000e6
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+9
+4
+3 3 3 1
+0.0 0.52428800000000000000e6 -0.10485760000000000000e7 0.0 0.52428800000000000000e6 0.52428800000000000000e6 -0.10485760000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6
+0 1 1 1 0.52428800000000000000e6
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+6 1 1 3 -0.26214400000000000000e6
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+7 1 3 3 -0.10485760000000000000e7
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+8 3 2 2 0.52428800000000000000e6
+9 3 1 2 -0.26214400000000000000e6
+9 4 1 1 0.52428800000000000000e6
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+25
+5
+6 1 3 3 3
+0.0 0.0 0.13107200000000000000e6 0.0 0.0 0.0 -0.10485760000000000000e7 0.13107200000000000000e6 -0.26214400000000000000e6 0.13107200000000000000e6 0.13107200000000000000e6 0.0 0.13107200000000000000e6 0.0 0.13107200000000000000e6 0.13107200000000000000e6 0.0 0.13107200000000000000e6 0.0 0.13107200000000000000e6 0.0 0.0 -0.39321600000000000000e6 0.0 0.13107200000000000000e6
+0 1 1 1 0.52428800000000000000e6
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+24 5 2 3 0.52428800000000000000e6
+25 1 5 6 -0.26214400000000000000e6
+25 5 3 3 0.52428800000000000000e6
+*** ANSWER ***
+-4.113697398682738004e-09 8.215094087406949078e-09 1.106563519105026888e-08 -6.332908356568953188e-09 -2.931819407167173368e-05 -2.931818908533051569e-05 -5.000000074902808400e-01 1.106405735886701213e-08 -4.451398475879184303e-09 9.999643968605362865e-01 5.868338520830287551e-09 -1.415827732183235363e-09 8.903640791049248497e-09 -7.865132682789377989e-09 8.902267568543103993e-09 5.889851427419620259e-09 -1.423050516012667677e-09 8.903577047039871176e-09 -7.862722209332731223e-09 1.916770858206847272e-09 -2.334896842407189883e-12 -4.728327014591874540e-13 5.419760765973143563e-09 -5.673174330751571568e-09 5.419709023311579812e-09
+1 1 1 1 5.145820320597975853e-03
+1 1 1 2 -1.538349733204534900e-03
+1 1 1 3 -2.156762181760575343e-03
+1 1 1 4 -1.543989212589488933e-03
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+1 1 1 6 -2.154287943343585060e-03
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+1 1 4 4 5.933959598042677815e-03
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+1 5 1 2 -1.224158395711980769e-06
+1 5 1 3 -2.479005113826344719e-07
+1 5 2 2 2.974722625947537249e-03
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+1 5 3 3 2.974695497890991313e-03
+2 1 1 1 1.249995407955173832e+00
+2 1 1 2 1.365127722796842358e+00
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+2 1 4 5 6.025682974288950611e+00
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+2 1 5 5 3.435903369964215926e+03
+2 1 5 6 3.435781122368971864e+03
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+2 2 1 1 1.279963716390136885e-08
+2 3 1 1 1.615127722792867315e+00
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+2 3 2 2 6.275700356768556532e+00
+2 3 2 3 6.025697877918420708e+00
+2 3 3 3 6.275682968722814614e+00
+2 4 1 1 1.612163827043817665e+00
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+2 4 2 2 6.275697877761073684e+00
+2 4 2 3 6.025682968550636787e+00
+2 4 3 3 6.275662481899622058e+00
+2 5 1 1 2.568434463701084081e+00
+2 5 1 2 6.025697877856011964e+00
+2 5 1 3 6.025682968701328690e+00
+2 5 2 2 3.436025613004531351e+03
+2 5 2 3 3.435653369841461881e+03
+2 5 3 3 3.436031122293553381e+03
+*** END ***
+*** REQUEST ***
+""
+2
+3
+2 1 1
+0.15728640000000000000e7 0.52428800000000000000e6
+0 1 1 2 0.52428800000000000000e6
+0 1 2 2 -0.10485760000000000000e7
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+1 1 1 2 -0.52428800000000000000e6
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+1 2 1 1 0.10485760000000000000e7
+2 1 1 2 -0.52428800000000000000e6
+2 3 1 1 0.10485760000000000000e7
+*** ANSWER ***
+3.333333330935131511e-01 -1.478241289070492609e-11
+1 1 1 1 3.495253334203167469e+05
+1 1 1 2 -6.990506665331815602e+05
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+2 1 1 2 9.999999992811959837e-01
+2 1 2 2 4.999999998586800998e-01
+2 2 1 1 3.464905364927463821e-10
+2 3 1 1 1.499999999281195651e+00
+*** END ***
+*** REQUEST ***
+""
+1
+6
+1 1 1 1 1 1
+-0.10485760000000000000e7
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+1 4 1 1 -0.10485760000000000000e7
+1 5 1 1 0.10485760000000000000e7
+1 6 1 1 -0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+16
+16
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+16 1 4 5 -0.26214400000000000000e6
+16 6 1 1 0.52428800000000000000e6
+16 15 1 1 0.52428800000000000000e6
+*** ANSWER ***
+-2.510945831846816927e-10 7.584564995981076880e-11 -3.980910209918642198e-10 1.344946711011189854e-10 -8.782665206711593718e-11 -5.852309807939336404e-11 -6.669457535662038939e-11 9.130977785251912681e-10 9.999999956372092047e-01 9.999999994808139725e-01 -8.835712425264707961e-11 9.999999984230395489e-01 4.308129358900289983e-10 9.999999981672165195e-01 -8.823106083428535072e-11 -1.165612788739154225e-10
+1 1 1 1 2.212302206669363239e-04
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+1 1 2 2 2.915950003628733217e-04
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+2 15 1 1 1.093937070702268199e+00
+2 16 1 1 7.097821616243046305e-01
+*** END ***
+*** REQUEST ***
+""
+1
+6
+1 1 1 1 1 1
+0.10485760000000000000e7
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+1 4 1 1 -0.10485760000000000000e7
+1 5 1 1 0.10485760000000000000e7
+1 6 1 1 -0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+16
+16
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+16 1 4 5 -0.26214400000000000000e6
+16 6 1 1 -0.52428800000000000000e6
+16 15 1 1 0.52428800000000000000e6
+*** ANSWER ***
+5.971802404885320773e-11 -3.502156570007520369e-10 1.582565515461167484e-10 1.581307857780074475e-10 -1.929547772322441932e-10 9.017698861213426687e-11 1.396679925039875230e-10 7.818207487653054736e-11 9.999999998832547199e-01 9.999999980736424821e-01 3.275620235594100367e-11 9.999999994214049392e-01 3.296132408197630990e-11 9.999999991834543911e-01 1.474133598215077482e-10 4.368570581248094817e-10
+1 1 1 1 2.199547425220330782e-04
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+2 15 1 1 1.032706160331063439e+00
+2 16 1 1 1.644477055802265664e+00
+*** END ***
+*** REQUEST ***
+""
+1
+1
+7
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
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+1 1 5 5 0.0
+1 1 6 6 0.0
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+1
+1
+7
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+1 1 7 7 0.10000000000000000000e1
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+2
+1
+8
+0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1 0.10000000000000000000e1
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+2
+1
+8
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+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+2
+1
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+Infeasible
+*** END ***
+*** REQUEST ***
+""
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+Infeasible
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+*** REQUEST ***
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+Infeasible
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+*** REQUEST ***
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+Infeasible
+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
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+*** REQUEST ***
+""
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+*** ANSWER ***
+Failure
+*** END ***
+*** REQUEST ***
+""
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+*** END ***
+*** REQUEST ***
+""
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+*** ANSWER ***
+Failure
+*** END ***
+*** REQUEST ***
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+2 3 2 2 1.577350183915906534e+00
+2 3 2 3 -5.093597884469405757e-03
+2 3 2 4 7.563155554311366017e-08
+2 3 3 3 1.000664225665719220e+00
+2 3 3 4 5.093637134632639923e-03
+2 3 4 4 1.577350204179726045e+00
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+2 5 1 2 5.773502768886699110e-01
+2 5 1 3 2.801943516876615048e-08
+2 5 1 4 5.773502602186050270e-01
+2 5 2 2 4.226498160840916896e-01
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+2 5 2 4 -7.563155467628118543e-08
+2 5 3 3 9.993357743342811128e-01
+2 5 3 4 -5.093637134632782171e-03
+2 5 4 4 4.226497958202757865e-01
+2 6 1 1 4.226497668634069393e-01
+2 7 1 1 9.999999833299334506e-01
+*** END ***
+*** REQUEST ***
+""
+2
+4
+1 1 1 1
+0.15728640000000000000e7 0.10485760000000000000e7
+0 2 1 1 -0.10485760000000000000e7
+0 4 1 1 -0.10485760000000000000e7
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+1 4 1 1 0.10485760000000000000e7
+2 2 1 1 0.10485760000000000000e7
+2 3 1 1 0.10485760000000000000e7
+*** ANSWER ***
+-8.033537119682993312e-10 -8.033532523347130644e-10
+1 1 1 1 9.639215222160258208e-10
+1 2 1 1 1.048575999157623970e+06
+1 3 1 1 1.445882272036933453e-09
+1 4 1 1 1.048576000000000931e+06
+2 1 1 1 1.499999999685651009e+00
+2 2 1 1 1.378900983392931975e-15
+2 3 1 1 9.999999999999862332e-01
+2 4 1 1 1.378900796134651217e-15
+*** END ***
+*** REQUEST ***
+""
+1
+3
+1 1 1
+0.10485760000000000000e7
+0 1 1 1 0.10485760000000000000e7
+1 1 1 1 0.10485760000000000000e7
+1 2 1 1 -0.10485760000000000000e7
+1 3 1 1 0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+5
+5
+4 1 1 1 1
+0.10485760000000000000e7 0.0 0.52428800000000000000e6 0.52428800000000000000e6 0.0
+0 2 1 1 -0.52428800000000000000e6
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+3 1 1 2 -0.52428800000000000000e6
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+5 1 1 2 -0.52428800000000000000e6
+5 1 1 4 0.26214400000000000000e6
+5 1 3 4 0.52428800000000000000e6
+5 1 4 4 -0.52428800000000000000e6
+5 5 1 1 0.52428800000000000000e6
+*** ANSWER ***
+-1.338594917701584393e-10 -4.876570677399720908e-12 -8.432248596379257249e-11 -1.376003305176662146e-10 6.303077531793304895e-11
+1 1 1 1 1.961387163584582007e-06
+1 1 1 2 1.116298839109634367e-05
+1 1 1 3 -2.556727487312544875e-06
+1 1 1 4 -3.024766708235593078e-06
+1 1 2 2 7.214231238477719979e-05
+1 1 3 3 2.793304486379264481e-05
+1 1 3 4 3.304627912988848237e-05
+1 1 4 4 3.909603325488893426e-05
+1 2 1 1 5.242879998907233821e+05
+1 3 1 1 1.102983309069068926e-10
+1 4 1 1 1.833803270175834998e-04
+1 5 1 1 1.051885915146662243e-04
+2 1 1 1 1.999999999825280872e+00
+2 1 1 2 -3.095056099254819282e-01
+2 1 1 3 8.388821521212311283e-02
+2 1 1 4 8.388917358587567874e-02
+2 1 2 2 4.789927494245199008e-02
+2 1 2 3 -1.307058076260208049e-02
+2 1 2 4 -1.290714134044862460e-02
+2 1 3 3 2.971005649372479018e-01
+2 1 3 4 -2.447309307272341194e-01
+2 1 4 4 2.134402019028047992e-01
+2 2 1 1 2.103712716147778344e-16
+2 3 1 1 1.000000958427416542e+00
+2 4 1 1 9.583793370118670507e-07
+2 5 1 1 1.669900717227676154e-06
+*** END ***
+*** REQUEST ***
+""
+4
+2
+3 1
+-0.52428800000000000000e6 0.52428800000000000000e6 0.10485760000000000000e7 0.0
+0 1 2 2 0.10485760000000000000e7
+0 1 3 3 -0.10485760000000000000e7
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+1 1 2 3 0.52428800000000000000e6
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+3 2 1 1 0.10485760000000000000e7
+4 1 1 2 -0.10485760000000000000e7
+4 1 1 3 0.10485760000000000000e7
+*** ANSWER ***
+9.999995669872646653e-01 9.999987009619675238e-01 -8.660253659925441563e-07 0.000000000000000000e+00
+1 1 1 1 3.962767353149487803e-08
+1 1 2 2 4.540467642000610149e-01
+1 1 2 3 4.540466709859902750e-01
+1 1 3 3 4.540468014726645185e-01
+1 2 1 1 1.048576000000039581e+06
+2 1 1 1 9.999999999999281686e-01
+2 1 2 2 2.500000307927105481e-01
+2 1 2 3 -2.499999692072846225e-01
+2 1 3 3 2.500000307927234822e-01
+2 2 1 1 5.333451642288094782e-14
+*** END ***
+*** REQUEST ***
+""
+4
+2
+3 1
+-0.52428800000000000000e6 0.52428800000000000000e6 0.10485760000000000000e7 0.0
+0 1 2 2 -0.10485760000000000000e7
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+0 2 1 1 -0.10485760000000000000e7
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+3 2 1 1 0.10485760000000000000e7
+4 1 1 2 -0.10485760000000000000e7
+4 1 1 3 0.10485760000000000000e7
+*** ANSWER ***
+-9.999998331245307792e-01 -9.999999443745658523e-01 -1.112500350952176353e-07 0.000000000000000000e+00
+1 1 1 1 1.642036506765975901e-11
+1 1 2 2 5.832749536206643937e-02
+1 1 2 3 5.832705836608864658e-02
+1 1 3 3 5.832662143581340830e-02
+1 2 1 1 1.048576000000000000e+06
+2 1 1 1 9.999999999999996669e-01
+2 1 2 2 2.499998068521827044e-01
+2 1 2 3 -2.500000893194189722e-01
+2 1 3 3 2.500003721368480036e-01
+2 2 1 1 2.465190328815661892e-32
+*** END ***
+*** REQUEST ***
+""
+4
+2
+3 1
+-0.52428800000000000000e6 -0.52428800000000000000e6 0.10485760000000000000e7 0.0
+0 1 2 2 0.10485760000000000000e7
+0 1 3 3 -0.10485760000000000000e7
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+1 1 2 3 -0.52428800000000000000e6
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+3 2 1 1 0.10485760000000000000e7
+4 1 1 2 0.10485760000000000000e7
+4 1 1 3 0.10485760000000000000e7
+*** ANSWER ***
+9.999995669872646653e-01 -9.999987009619675238e-01 -8.660253659925441563e-07 0.000000000000000000e+00
+1 1 1 1 3.962767353149487803e-08
+1 1 2 2 4.540467642000610149e-01
+1 1 2 3 -4.540466709859902750e-01
+1 1 3 3 4.540468014726645185e-01
+1 2 1 1 1.048576000000039581e+06
+2 1 1 1 9.999999999999281686e-01
+2 1 2 2 2.500000307927105481e-01
+2 1 2 3 2.499999692072846225e-01
+2 1 3 3 2.500000307927234822e-01
+2 2 1 1 5.333451642288094782e-14
+*** END ***
+*** REQUEST ***
+""
+4
+2
+3 1
+-0.52428800000000000000e6 -0.52428800000000000000e6 0.10485760000000000000e7 0.0
+0 1 2 2 -0.10485760000000000000e7
+0 1 3 3 0.10485760000000000000e7
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+1 1 2 3 -0.52428800000000000000e6
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+2 1 2 3 -0.52428800000000000000e6
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+3 2 1 1 0.10485760000000000000e7
+4 1 1 2 0.10485760000000000000e7
+4 1 1 3 0.10485760000000000000e7
+*** ANSWER ***
+-9.999998331245307792e-01 9.999999443745658523e-01 -1.112500350952176353e-07 0.000000000000000000e+00
+1 1 1 1 1.642036506765975901e-11
+1 1 2 2 5.832749536206643937e-02
+1 1 2 3 -5.832705836608864658e-02
+1 1 3 3 5.832662143581340830e-02
+1 2 1 1 1.048576000000000000e+06
+2 1 1 1 9.999999999999996669e-01
+2 1 2 2 2.499998068521827044e-01
+2 1 2 3 2.500000893194189722e-01
+2 1 3 3 2.500003721368480036e-01
+2 2 1 1 2.465190328815661892e-32
+*** END ***
+*** REQUEST ***
+""
+1
+5
+1 1 1 1 1
+0.10485760000000000000e7
+0 1 1 1 0.10485760000000000000e7
+1 2 1 1 0.10485760000000000000e7
+1 4 1 1 0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+13
+11
+5 1 1 1 1 1 1 1 1 1 1
+0.15728640000000000000e7 -0.10485760000000000000e7 -0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7
+0 1 1 1 0.52428800000000000000e6
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+9 1 1 1 0.52428800000000000000e6
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+12 8 1 1 0.52428800000000000000e6
+12 10 1 1 0.52428800000000000000e6
+13 9 1 1 0.52428800000000000000e6
+13 11 1 1 0.52428800000000000000e6
+*** ANSWER ***
+1.491607500493158475e-10 -2.946260586897868525e-25 1.192686814972796844e-10 1.574303654274453910e-11 2.080232249849451083e-24 1.170819464678145350e+00 1.458414260046146013e-10 4.060381611148327209e-10 1.447214523119946250e+00 4.060381611148343752e-10 4.060381611148294122e-10 4.928738059904181593e-10 4.060381611148277578e-10
+1 1 1 1 2.344692080938835279e+05
+1 1 1 2 -1.544689070583509693e-19
+1 1 1 3 3.793786039487551898e+05
+1 1 1 4 6.253113848484577117e-05
+1 1 2 2 2.046271191861112615e-04
+1 1 2 3 3.810179772744665476e-19
+1 1 2 4 1.090640805809069009e-18
+1 1 3 3 6.138465956935486756e+05
+1 1 3 4 1.292039109975521780e-04
+1 1 4 4 2.763167071297943644e-04
+1 1 5 5 2.728361436002968432e-04
+1 2 1 1 4.092541694577598449e-04
+1 3 1 1 7.587572080938835861e+05
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+1 5 1 1 4.092541694577633143e-04
+1 6 1 1 6.138465957800056785e+05
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+1 8 1 1 3.297187790686018430e-04
+1 9 1 1 4.092541694577598449e-04
+1 10 1 1 4.547810560382933853e-04
+1 11 1 1 4.092541694577598449e-04
+2 1 1 1 5.236067975094374383e+00
+2 1 1 2 -4.180129510443609950e-16
+2 1 1 3 -3.236067975651311546e+00
+2 1 1 4 5.031018360597926398e-01
+2 1 2 2 1.999999999311909527e+00
+2 1 2 3 2.583501648248632324e-16
+2 1 2 4 5.150626177396930724e-17
+2 1 3 3 1.999999999311873555e+00
+2 1 3 4 -3.109408375486479303e-01
+2 1 4 4 1.499999999655955429e+00
+2 1 5 5 1.499999999655954985e+00
+2 2 1 1 1.000000000000000222e+00
+2 3 1 1 5.567308407420794632e-10
+2 4 1 1 1.000000000000000000e+00
+2 5 1 1 9.999999999999996669e-01
+2 6 1 1 6.880904095754841013e-10
+2 7 1 1 1.000000000000000000e+00
+2 8 1 1 1.503101836059808738e+00
+2 9 1 1 9.999999999999998890e-01
+2 10 1 1 8.078390014888369164e-01
+2 11 1 1 1.000000000000000222e+00
+*** END ***
+*** REQUEST ***
+""
+1
+5
+1 1 1 1 1
+0.15728640000000000000e7
+0 1 1 1 0.10485760000000000000e7
+1 1 1 1 0.10485760000000000000e7
+1 2 1 1 0.10485760000000000000e7
+1 5 1 1 0.10485760000000000000e7
+*** ANSWER ***
+1.000000001957216389e+00
+1 1 1 1 3.452177815527975729e-03
+1 2 1 1 1.048576003452177858e+06
+1 3 1 1 1.399887753448717312e-03
+1 4 1 1 1.399887753448717312e-03
+1 5 1 1 1.048576003452177858e+06
+2 1 1 1 1.499999999999996891e+00
+2 2 1 1 1.625838482485675356e-15
+2 3 1 1 2.922314168167987170e+00
+2 4 1 1 2.922314168167987170e+00
+2 5 1 1 1.625838482485675356e-15
+*** END ***
+*** REQUEST ***
+""
+10
+8
+5 1 1 1 1 1 1 1
+0.26214400000000000000e6 0.78643200000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.0 -0.52428800000000000000e6 0.10485760000000000000e7 0.0 -0.26214400000000000000e6 0.52428800000000000000e6
+0 1 3 3 -0.10485760000000000000e7
+0 1 4 4 0.52428800000000000000e6
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+9 1 1 4 0.26214400000000000000e6
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+9 1 4 4 0.52428800000000000000e6
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+9 3 1 1 0.52428800000000000000e6
+10 1 3 4 0.26214400000000000000e6
+10 6 1 1 0.52428800000000000000e6
+10 7 1 1 0.52428800000000000000e6
+*** ANSWER ***
+-9.999999995891341031e-01 -3.803473486621178888e-10 -6.700393916482747952e-12 -5.428871525357892679e-12 4.357318402697323595e-11 1.224368895784648765e-10 -1.397522156751196915e-10 -1.881197163293053418e-10 1.961501144259765512e-10 -2.678331179220082914e-10
+1 1 1 1 6.945594704874666694e-05
+1 1 1 2 -3.512936125684906958e-06
+1 1 1 3 -2.846292194286838837e-06
+1 1 1 4 5.141957559608319704e-05
+1 1 2 2 2.917123952912454438e-04
+1 1 2 3 6.419219196331419318e-05
+1 1 2 4 -7.327040965187715284e-05
+1 1 3 3 1.938191092966602865e-04
+1 1 3 4 -7.021084486454694153e-05
+1 1 4 4 3.328611961756211546e-04
+1 1 5 5 1.702385879492527253e-04
+1 2 1 1 5.242879999666168005e+05
+1 3 1 1 3.717066489762766573e-04
+1 4 1 1 1.293525507317268286e-04
+1 5 1 1 1.223266784803576923e-04
+1 6 1 1 1.341383924435904373e-04
+1 7 1 1 1.284458080550170307e-04
+1 8 1 1 1.404831138574836116e-04
+2 1 1 1 9.999999999048130306e-01
+2 1 1 2 -9.791805858089613901e-02
+2 1 1 3 -7.495940148985721918e-02
+2 1 1 4 -1.761119473870640384e-01
+2 1 2 2 2.862965238970243131e-01
+2 1 2 3 -6.789572938328512774e-02
+2 1 2 4 1.173483178028186941e-01
+2 1 3 3 3.931482619485121011e-01
+2 1 3 4 1.011591097635078512e-01
+2 1 4 4 2.862965238970242576e-01
+2 1 5 5 3.931482619485121566e-01
+2 2 1 1 9.518727013297796622e-11
+2 3 1 1 1.761119474822513409e-01
+2 4 1 1 4.020819414191039165e-01
+2 5 1 1 4.805697407780772368e-01
+2 6 1 1 4.250405985101427531e-01
+2 7 1 1 4.738002917263492431e-01
+2 8 1 1 4.321042706167148584e-01
+*** END ***
+*** REQUEST ***
+""
+10
+8
+5 1 1 1 1 1 1 1
+0.26214400000000000000e6 0.26214400000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.0 -0.52428800000000000000e6 0.10485760000000000000e7 0.0 0.26214400000000000000e6 0.52428800000000000000e6
+0 1 3 3 0.10485760000000000000e7
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+7 1 2 4 0.52428800000000000000e6
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+8 1 3 3 -0.52428800000000000000e6
+8 1 5 5 0.52428800000000000000e6
+9 1 1 4 0.26214400000000000000e6
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+9 3 1 1 0.52428800000000000000e6
+10 1 3 4 0.26214400000000000000e6
+10 6 1 1 0.52428800000000000000e6
+10 7 1 1 0.52428800000000000000e6
+*** ANSWER ***
+9.999999992578435526e-01 -3.803621179669960753e-10 -6.700611093044749451e-12 -5.429040383980874669e-12 4.357544632633943844e-11 1.224427165113750327e-10 -1.397590492693696129e-10 -1.881286560854844638e-10 1.961553626130812178e-10 -2.678452895980398204e-10
+1 1 1 1 6.945800898995211844e-05
+1 1 1 2 -3.513049988750245600e-06
+1 1 1 3 -2.846380724836564818e-06
+1 1 1 4 5.142095137684356276e-05
+1 1 2 2 2.917233866981758933e-04
+1 1 2 3 6.419524695431579314e-05
+1 1 2 4 -7.327399242333925561e-05
+1 1 3 3 1.938259237923606500e-04
+1 1 3 4 -7.021403559638855069e-05
+1 1 4 4 3.328737160779339510e-04
+1 1 5 5 1.702437062528860783e-04
+1 2 1 1 5.242879999666161020e+05
+1 3 1 1 3.717192058483196823e-04
+1 4 1 1 1.293554182254532357e-04
+1 5 1 1 1.223293182479527445e-04
+1 6 1 1 1.341419933515285851e-04
+1 7 1 1 1.284492319018545881e-04
+1 8 1 1 1.404868091860003200e-04
+2 1 1 1 9.999999999048114763e-01
+2 1 1 2 -9.791875554850019980e-02
+2 1 1 3 -7.495921678613150230e-02
+2 1 1 4 -1.761120526754002824e-01
+2 1 2 2 2.862954232683553313e-01
+2 1 2 3 -6.789625167944521311e-02
+2 1 2 4 1.173501309850062402e-01
+2 1 3 3 3.931477116341772216e-01
+2 1 3 4 1.011600384885519704e-01
+2 1 4 4 2.862954232683553313e-01
+2 1 5 5 3.931477116341773326e-01
+2 2 1 1 9.518835915348206933e-11
+2 3 1 1 1.761120527705894168e-01
+2 4 1 1 4.020812444514997308e-01
+2 5 1 1 4.805686245634940290e-01
+2 6 1 1 4.250407832138684561e-01
+2 7 1 1 4.737991782975795041e-01
+2 8 1 1 4.321037483205548702e-01
+*** END ***
+*** REQUEST ***
+""
+13
+11
+5 1 1 1 1 1 1 1 1 1 1
+0.15728640000000000000e7 -0.10485760000000000000e7 -0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.10485760000000000000e7 0.0 0.10485760000000000000e7 0.10485760000000000000e7 0.10485760000000000000e7
+0 1 1 1 0.52428800000000000000e6
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+7 1 4 4 -0.52428800000000000000e6
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+8 1 2 3 0.26214400000000000000e6
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+8 4 1 1 0.52428800000000000000e6
+9 1 1 1 0.52428800000000000000e6
+9 1 1 3 -0.26214400000000000000e6
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+10 1 2 3 -0.26214400000000000000e6
+10 4 1 1 -0.52428800000000000000e6
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+11 4 1 1 0.52428800000000000000e6
+11 7 1 1 0.52428800000000000000e6
+12 1 3 4 -0.26214400000000000000e6
+12 8 1 1 0.52428800000000000000e6
+12 10 1 1 0.52428800000000000000e6
+13 9 1 1 0.52428800000000000000e6
+13 11 1 1 0.52428800000000000000e6
+*** ANSWER ***
+1.492389361104177029e-10 -5.414006260063542034e-26 1.193034345414183999e-10 1.580132269315673874e-11 -3.822602920229432166e-25 1.170819464637501417e+00 1.459189285079053882e-10 4.061540963088140009e-10 1.447214523160652133e+00 4.061540963088156553e-10 4.061540963088156553e-10 4.930152203813611015e-10 4.061540963088140009e-10
+1 1 1 1 2.344692081152248720e+05
+1 1 1 2 -2.838498514076194326e-20
+1 1 1 3 -3.793786039594259928e+05
+1 1 1 4 6.254935908885117003e-05
+1 1 2 2 2.046573439116062404e-04
+1 1 2 3 -1.807183432951896983e-19
+1 1 2 4 -2.004144839841248531e-19
+1 1 3 3 6.138465956722392002e+05
+1 1 3 4 -1.292409819316515246e-04
+1 1 4 4 2.763577235208210248e-04
+1 1 5 5 2.728764432290099393e-04
+1 2 1 1 4.093146188850118466e-04
+1 3 1 1 7.587572081152248429e+05
+1 4 1 1 4.093146188850118466e-04
+1 5 1 1 4.093146188850118466e-04
+1 6 1 1 6.138465957587677985e+05
+1 7 1 1 4.093146188850118466e-04
+1 8 1 1 3.297561457250566472e-04
+1 9 1 1 4.093146188850135814e-04
+1 10 1 1 4.548548639027594209e-04
+1 11 1 1 4.093146188850118466e-04
+2 1 1 1 5.236067975094174543e+00
+2 1 1 2 -1.034045711543959444e-15
+2 1 1 3 3.236067975651042428e+00
+2 1 1 4 5.031158753095015257e-01
+2 1 2 2 1.999999999311752097e+00
+2 1 2 3 -6.390572893185565781e-16
+2 1 2 4 -2.752195281539649504e-16
+2 1 3 3 1.999999999311723231e+00
+2 1 3 4 3.109495151127604218e-01
+2 1 4 4 1.499999999655875937e+00
+2 1 5 5 1.499999999655876382e+00
+2 2 1 1 1.000000000000000888e+00
+2 3 1 1 5.568581590258357525e-10
+2 4 1 1 9.999999999999995559e-01
+2 5 1 1 9.999999999999991118e-01
+2 6 1 1 6.882477664469128551e-10
+2 7 1 1 1.000000000000000222e+00
+2 8 1 1 1.503115875309488425e+00
+2 9 1 1 1.000000000000000222e+00
+2 10 1 1 8.078336398032637256e-01
+2 11 1 1 9.999999999999994449e-01
+*** END ***
+*** REQUEST ***
+""
+10
+8
+5 1 1 1 1 1 1 1
+0.26214400000000000000e6 0.78643200000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.0 -0.52428800000000000000e6 -0.10485760000000000000e7 0.0 -0.26214400000000000000e6 0.52428800000000000000e6
+0 1 3 3 -0.10485760000000000000e7
+0 1 4 4 0.52428800000000000000e6
+0 2 1 1 -0.52428800000000000000e6
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+7 1 2 4 0.52428800000000000000e6
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+7 5 1 1 -0.10485760000000000000e7
+8 1 3 3 -0.52428800000000000000e6
+8 1 5 5 0.52428800000000000000e6
+9 1 1 4 -0.26214400000000000000e6
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+9 3 1 1 0.52428800000000000000e6
+10 1 3 4 -0.26214400000000000000e6
+10 6 1 1 0.52428800000000000000e6
+10 7 1 1 0.52428800000000000000e6
+*** ANSWER ***
+-9.999999995884889525e-01 -3.810702490824998314e-10 -6.736049984565948920e-12 -5.444970347363611579e-12 4.367510600526014834e-11 1.227416529920419783e-10 1.401233411982328640e-10 -1.886161028276272925e-10 1.964405220582090356e-10 -2.684361283113760051e-10
+1 1 1 1 6.957824710356660253e-05
+1 1 1 2 -3.531630174308112227e-06
+1 1 1 3 -2.854732613478573188e-06
+1 1 1 4 -5.149570421442714943e-05
+1 1 2 2 2.922671398318177002e-04
+1 1 2 3 6.435197576389170473e-05
+1 1 2 4 7.346498631013911179e-05
+1 1 3 3 1.941947017891744801e-04
+1 1 3 4 7.036892042005735148e-05
+1 1 4 4 3.335021955722895434e-04
+1 1 5 5 1.704796465352414331e-04
+1 2 1 1 5.242879999665868236e+05
+1 3 1 1 3.723602142833857057e-04
+1 4 1 1 1.295020935828698413e-04
+1 5 1 1 1.224388332342540506e-04
+1 6 1 1 1.343404302413743652e-04
+1 7 1 1 1.286309650144171375e-04
+1 8 1 1 1.406648543267486479e-04
+2 1 1 1 9.999999999048063692e-01
+2 1 1 2 -9.795776109657357289e-02
+2 1 1 3 -7.486293410754249478e-02
+2 1 1 4 1.760544474048320318e-01
+2 1 2 2 2.860583275573886364e-01
+2 1 2 3 -6.792470349951823527e-02
+2 1 2 4 -1.175072693384005135e-01
+2 1 3 3 3.930291637786945125e-01
+2 1 3 4 -1.012001156063697394e-01
+2 1 4 4 2.860583275573886919e-01
+2 1 5 5 3.930291637786945680e-01
+2 2 1 1 9.519245368151487941e-11
+2 3 1 1 1.760544475000250519e-01
+2 4 1 1 4.020422389034264410e-01
+2 5 1 1 4.804504917581729484e-01
+2 6 1 1 4.251370658924574775e-01
+2 7 1 1 4.736628185011726999e-01
+2 8 1 1 4.320752965004817647e-01
+*** END ***
+*** REQUEST ***
+""
+10
+8
+5 1 1 1 1 1 1 1
+0.26214400000000000000e6 0.26214400000000000000e6 -0.52428800000000000000e6 -0.52428800000000000000e6 0.0 -0.52428800000000000000e6 -0.10485760000000000000e7 0.0 0.26214400000000000000e6 0.52428800000000000000e6
+0 1 3 3 0.10485760000000000000e7
+0 1 4 4 -0.52428800000000000000e6
+0 2 1 1 -0.52428800000000000000e6
+1 1 3 3 0.10485760000000000000e7
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+7 1 2 4 0.52428800000000000000e6
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+7 5 1 1 -0.10485760000000000000e7
+8 1 3 3 -0.52428800000000000000e6
+8 1 5 5 0.52428800000000000000e6
+9 1 1 4 -0.26214400000000000000e6
+9 1 3 3 0.10485760000000000000e7
+9 1 4 4 -0.52428800000000000000e6
+9 2 1 1 -0.52428800000000000000e6
+9 3 1 1 0.52428800000000000000e6
+10 1 3 4 -0.26214400000000000000e6
+10 6 1 1 0.52428800000000000000e6
+10 7 1 1 0.52428800000000000000e6
+*** ANSWER ***
+9.999999992564915230e-01 -3.810695576889143537e-10 -6.735625426342454187e-12 -5.444777627013238453e-12 4.367506358700158526e-11 1.227413030293301348e-10 1.401229005084607075e-10 -1.886153909364574320e-10 1.964397041031435087e-10 -2.684354364726813310e-10
+1 1 1 1 6.957817438412523987e-05
+1 1 1 2 -3.531407583526232621e-06
+1 1 1 3 -2.854631572511516762e-06
+1 1 1 4 -5.149548979241445196e-05
+1 1 2 2 2.922666823836324659e-04
+1 1 2 3 6.435179228264143771e-05
+1 1 2 4 7.346475526177984744e-05
+1 1 3 3 1.941943637436432425e-04
+1 1 3 4 7.036873905869457484e-05
+1 1 4 4 3.335015036236895630e-04
+1 1 5 5 1.704795845624373744e-04
+1 2 1 1 5.242879999665871728e+05
+1 3 1 1 3.723593502305598893e-04
+1 4 1 1 1.295016752892227258e-04
+1 5 1 1 1.224388601221695558e-04
+1 6 1 1 1.343401556733645440e-04
+1 7 1 1 1.286308925283409683e-04
+1 8 1 1 1.406647860804472426e-04
+2 1 1 1 9.999999999048075905e-01
+2 1 1 2 -9.795735713603917483e-02
+2 1 1 3 -7.486315305695728783e-02
+2 1 1 4 1.760541517543041112e-01
+2 1 2 2 2.860587828470143590e-01
+2 1 2 3 -6.792434344894913989e-02
+2 1 2 4 -1.175060159893176470e-01
+2 1 3 3 3.930293914235066244e-01
+2 1 3 4 -1.011994963720127400e-01
+2 1 4 4 2.860587828470145255e-01
+2 1 5 5 3.930293914235067909e-01
+2 2 1 1 9.519167358025126290e-11
+2 3 1 1 1.760541518494961044e-01
+2 4 1 1 4.020426428639607419e-01
+2 5 1 1 4.804513411467217221e-01
+2 6 1 1 4.251368469430427677e-01
+2 7 1 1 4.736636566849445895e-01
+2 8 1 1 4.320756565510509017e-01
+*** END ***
+*** REQUEST ***
+""
+1
+4
+1 1 1 1
+0.10485760000000000000e7
+0 1 1 1 0.52428800000000000000e6
+1 1 1 1 0.10485760000000000000e7
+1 2 1 1 0.52428800000000000000e6
+1 3 1 1 0.52428800000000000000e6
+*** ANSWER ***
+5.000000006943153830e-01
+1 1 1 1 1.290417214877562224e-03
+1 2 1 1 2.621440009263960528e+05
+1 3 1 1 2.621440009263960528e+05
+1 4 1 1 5.623748076465434273e-04
+2 1 1 1 9.999999999999984457e-01
+2 2 1 1 1.665972352747017299e-15
+2 3 1 1 1.665972352747017299e-15
+2 4 1 1 1.637537031929143128e+00
+*** END ***
+*** REQUEST ***
+""
+1
+4
+1 1 1 1
+0.15728640000000000000e7
+0 1 1 1 0.10485760000000000000e7
+1 1 1 1 0.10485760000000000000e7
+1 2 1 1 0.52428800000000000000e6
+1 3 1 1 0.10485760000000000000e7
+1 4 1 1 -0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+7
+7
+3 1 1 1 1 1 1
+0.10485760000000000000e7 0.52428800000000000000e6 0.26214400000000000000e6 0.10485760000000000000e7 0.13107200000000000000e7 0.52428800000000000000e6 0.52428800000000000000e6
+0 1 1 1 0.10485760000000000000e7
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+5 1 1 1 0.10485760000000000000e7
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+6 1 1 2 -0.52428800000000000000e6
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+7 1 1 2 0.52428800000000000000e6
+7 1 2 3 -0.52428800000000000000e6
+7 7 1 1 0.10485760000000000000e7
+*** ANSWER ***
+9.999999985586283113e-01 -9.282233207833762598e-10 2.416410040619999275e-09 7.287384010613641448e-10 1.000000001150653572e+00 -1.678412777448631064e-10 9.999999957510178339e-01
+1 1 1 1 2.123588660274164375e-03
+1 1 1 2 -1.769654364154091275e-03
+1 1 1 3 -9.733126968137495449e-04
+1 1 2 2 3.450830535535617805e-03
+1 1 2 3 -1.769670706440063662e-04
+1 1 3 3 1.681178558413772006e-03
+1 2 1 1 1.048576000173377106e+06
+1 3 1 1 1.048576002123588696e+06
+1 4 1 1 5.242880005434158957e+05
+1 5 1 1 7.410466251298562790e-04
+1 6 1 1 1.048575998138758354e+06
+1 7 1 1 1.048575996461660252e+06
+2 1 1 1 2.749999992995243225e+00
+2 1 1 2 1.499999995096669370e+00
+2 1 1 3 1.749999994396194358e+00
+2 1 2 2 1.249999997198100399e+00
+2 1 2 3 9.999999964976236111e-01
+2 1 3 3 1.999999994396199687e+00
+2 2 1 1 1.400950902881645464e-09
+2 3 1 1 1.400951113825400542e-09
+2 4 1 1 2.801898309253689249e-09
+2 5 1 1 1.999999995096668037e+00
+2 6 1 1 1.400952195814864889e-09
+2 7 1 1 1.400955085529339772e-09
+*** END ***
+*** REQUEST ***
+""
+1
+4
+1 1 1 1
+-0.10485760000000000000e7
+0 1 1 1 0.52428800000000000000e6
+1 1 1 1 0.52428800000000000000e6
+1 2 1 1 -0.52428800000000000000e6
+1 3 1 1 0.52428800000000000000e6
+1 4 1 1 -0.10485760000000000000e7
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+7
+7
+3 1 1 1 1 1 1
+-0.15728640000000000000e7 0.52428800000000000000e6 -0.52428800000000000000e6 0.78643200000000000000e6 0.10485760000000000000e7 0.78643200000000000000e6 0.26214400000000000000e6
+0 1 1 1 0.10485760000000000000e7
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+3 1 2 3 -0.10485760000000000000e7
+3 2 1 1 -0.10485760000000000000e7
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+4 1 2 3 -0.26214400000000000000e6
+4 1 3 3 0.10485760000000000000e7
+4 6 1 1 0.52428800000000000000e6
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+5 1 1 2 -0.52428800000000000000e6
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+6 1 1 2 -0.26214400000000000000e6
+6 2 1 1 0.52428800000000000000e6
+6 5 1 1 0.10485760000000000000e7
+7 1 1 2 0.26214400000000000000e6
+7 1 2 3 -0.52428800000000000000e6
+7 2 1 1 -0.52428800000000000000e6
+7 7 1 1 0.10485760000000000000e7
+*** ANSWER ***
+-2.122682326267485209e+00 7.752558743508156103e-02 1.165856920741376257e+00 9.814639206878961880e-03 1.612372975707343281e+00 -5.204790215550311268e-10 3.519523024615122119e-08
+1 1 1 1 6.421196079141121591e+05
+1 1 1 2 -8.859935285101566697e+05
+1 1 1 3 8.129147037032808294e+04
+1 1 2 2 1.222489589062118437e+06
+1 1 2 3 -1.121655822818670131e+05
+1 1 3 3 1.029139765980135235e+04
+1 2 1 1 1.084595610608764226e+06
+1 3 1 1 1.690695607914112275e+06
+1 4 1 1 1.003304158963754307e+06
+1 5 1 1 1.993047227803988741e-03
+1 6 1 1 2.230939443047560286e+06
+1 7 1 1 3.944368278889842649e-02
+2 1 1 1 4.259591772956758504e+00
+2 1 1 2 3.259591775595432228e+00
+2 1 1 3 1.879795885741197825e+00
+2 1 2 2 2.499999987441589688e+00
+2 1 2 3 1.499999989441199277e+00
+2 1 3 3 1.499999993720805946e+00
+2 2 1 1 4.113025632613441975e-09
+2 3 1 1 2.638667510379978050e-09
+2 4 1 1 4.446179952225849587e-09
+2 5 1 1 2.379795885741203598e+00
+2 6 1 1 1.999588384178727381e-09
+2 7 1 1 1.202041036999986628e-01
+*** END ***
+*** REQUEST ***
+""
+1
+4
+1 1 1 1
+0.15728640000000000000e7
+0 1 1 1 0.52428800000000000000e6
+1 1 1 1 0.10485760000000000000e7
+1 2 1 1 0.52428800000000000000e6
+1 3 1 1 0.52428800000000000000e6
+1 4 1 1 -0.52428800000000000000e6
+*** ANSWER ***
+Infeasible
+*** END ***
+*** REQUEST ***
+""
+7
+7
+3 1 1 1 1 1 1
+0.10485760000000000000e7 0.10485760000000000000e7 0.78643200000000000000e6 0.52428800000000000000e6 -0.52428800000000000000e6 0.78643200000000000000e6 -0.26214400000000000000e6
+0 1 1 2 -0.39321600000000000000e6
+0 1 2 3 -0.13107200000000000000e6
+0 2 1 1 -0.78643200000000000000e6
+0 4 1 1 -0.26214400000000000000e6
+0 6 1 1 -0.52428800000000000000e6
+1 1 1 1 0.52428800000000000000e6
+1 1 1 2 0.39321600000000000000e6
+1 1 2 3 0.13107200000000000000e6
+1 2 1 1 0.78643200000000000000e6
+1 4 1 1 0.26214400000000000000e6
+1 6 1 1 0.52428800000000000000e6
+2 1 1 2 0.26214400000000000000e6
+2 1 1 3 0.52428800000000000000e6
+2 1 2 3 0.26214400000000000000e6
+2 2 1 1 0.52428800000000000000e6
+2 4 1 1 0.52428800000000000000e6
+2 6 1 1 0.10485760000000000000e7
+3 1 1 2 0.26214400000000000000e6
+3 1 2 2 0.52428800000000000000e6
+3 1 2 3 -0.26214400000000000000e6
+3 2 1 1 0.52428800000000000000e6
+3 4 1 1 0.52428800000000000000e6
+4 1 1 2 0.13107200000000000000e6
+4 1 2 3 -0.13107200000000000000e6
+4 1 3 3 0.52428800000000000000e6
+4 2 1 1 0.26214400000000000000e6
+4 4 1 1 0.26214400000000000000e6
+5 1 1 2 -0.65536000000000000000e6
+5 1 2 3 -0.13107200000000000000e6
+5 2 1 1 -0.78643200000000000000e6
+5 3 1 1 0.52428800000000000000e6
+5 4 1 1 -0.26214400000000000000e6
+5 6 1 1 -0.52428800000000000000e6
+6 1 1 2 0.13107200000000000000e6
+6 1 2 3 0.13107200000000000000e6
+6 2 1 1 0.26214400000000000000e6
+6 4 1 1 0.26214400000000000000e6
+6 5 1 1 0.52428800000000000000e6
+6 6 1 1 0.52428800000000000000e6
+7 1 1 2 -0.13107200000000000000e6
+7 1 2 3 -0.39321600000000000000e6
+7 2 1 1 -0.26214400000000000000e6
+7 4 1 1 -0.26214400000000000000e6
+7 6 1 1 -0.52428800000000000000e6
+7 7 1 1 0.52428800000000000000e6
+*** ANSWER ***
+-7.608360275419644920e-10 -7.798072457369716546e-11 -8.013859884436968844e-10 -7.171668043536295414e-10 5.714285702070482920e-01 -7.988172012271727674e-10 1.428571434699175968e-01
+1 1 1 1 5.560274682077934530e-05
+1 1 1 2 -8.176870375087877353e-06
+1 1 1 3 -4.088435812529453948e-05
+1 1 2 2 3.434288891953024645e-05
+1 1 2 3 -1.635386148034894142e-06
+1 1 3 3 7.849799650774358199e-05
+1 2 1 1 2.995931426548591116e+05
+1 3 1 1 2.995931426712128450e+05
+1 4 1 1 7.489828527046926320e+04
+1 5 1 1 3.568967323170778479e-05
+1 6 1 1 1.497965713027546590e+05
+1 7 1 1 7.489828649005611078e+04
+2 1 1 1 1.357142856728937641e+00
+2 1 1 2 3.571428568738232445e-01
+2 1 1 3 7.142857137476383844e-01
+2 1 2 2 1.357142856728940306e+00
+2 1 2 3 2.142857143271021947e-01
+2 1 3 3 9.285714283644747047e-01
+2 2 1 1 1.448673344637826035e-10
+2 3 1 1 1.448673288269433621e-10
+2 4 1 1 5.794697349261452038e-10
+2 5 1 1 1.214285713747635498e+00
+2 6 1 1 2.897347029504898006e-10
+2 7 1 1 5.794683254243045175e-10
+*** END ***
+*** REQUEST ***
+""
+5
+5
+3 1 1 1 1
+0.10485760000000000000e7 -0.10485760000000000000e7 -0.52428800000000000000e6 0.0 0.10485760000000000000e7
+0 2 1 1 -0.52428800000000000000e6
+1 1 1 1 0.52428800000000000000e6
+1 2 1 1 0.52428800000000000000e6
+2 1 1 2 0.52428800000000000000e6
+2 4 1 1 -0.10485760000000000000e7
+3 1 2 2 -0.10485760000000000000e7
+3 1 3 3 0.52428800000000000000e6
+4 1 1 3 -0.26214400000000000000e6
+4 2 1 1 -0.52428800000000000000e6
+4 3 1 1 0.52428800000000000000e6
+5 1 2 3 -0.26214400000000000000e6
+5 4 1 1 0.52428800000000000000e6
+5 5 1 1 0.52428800000000000000e6
+*** ANSWER ***
+-4.457229613295930973e-10 6.115897346811394566e-17 1.833869924093994424e-10 -3.451031505601001684e-16 -4.457225765264029824e-10
+1 1 1 1 1.376100633449915924e-10
+1 1 1 2 3.206491588165052434e-11
+1 1 1 3 9.046672030042689854e-11
+1 1 2 2 4.139213860695481126e-05
+1 1 2 3 1.168434991009373834e-04
+1 1 3 3 3.298349370359715885e-04
+1 2 1 1 5.242880000000003492e+05
+1 3 1 1 2.336871566261909672e-04
+1 4 1 1 2.752279266958520360e-10
+1 5 1 1 3.393577580175436896e-10
+2 1 1 1 2.000000000038513637e+00
+2 1 1 2 1.679352122297247312e-04
+2 1 1 3 2.183096486070790850e-06
+2 1 2 2 5.333764953618103100e-01
+2 1 2 3 -1.886894755874139185e-01
+2 1 3 3 6.675299065681922217e-02
+2 2 1 1 5.248430535658322443e-16
+2 3 1 1 2.183106356807534618e-06
+2 4 1 1 1.000167935332526570e+00
+2 5 1 1 8.111425888609598012e-01
+*** END ***
diff --git a/test-suite/failure/circular_subtyping1.v b/test-suite/failure/circular_subtyping1.v
new file mode 100644
index 00000000..0b3a8688
--- /dev/null
+++ b/test-suite/failure/circular_subtyping1.v
@@ -0,0 +1,7 @@
+(* subtyping verification in presence of pseudo-circularity*)
+Module Type S. End S.
+Module Type T. Declare Module M:S. End T.
+
+Module N:S. End N.
+Module NN <: T. Module M:=N. End NN.
+Module P <: T with Module M:=NN := NN.
diff --git a/test-suite/failure/circular_subtyping2.v b/test-suite/failure/circular_subtyping2.v
new file mode 100644
index 00000000..3bacdc65
--- /dev/null
+++ b/test-suite/failure/circular_subtyping2.v
@@ -0,0 +1,8 @@
+(*subtyping verification in presence of pseudo-circularity at functor application *)
+Module Type S. End S.
+Module Type T. Declare Module M:S. End T.
+Module N:S. End N.
+
+Module F (X:S) (Y:T with Module M:=X). End F.
+
+Module G := F N N. \ No newline at end of file
diff --git a/test-suite/failure/fixpoint2.v b/test-suite/failure/fixpoint2.v
new file mode 100644
index 00000000..d2f02ea1
--- /dev/null
+++ b/test-suite/failure/fixpoint2.v
@@ -0,0 +1,6 @@
+(* Check Guard in proofs *)
+
+Goal nat->nat.
+fix f 1.
+intro n; apply f; assumption.
+Guarded.
diff --git a/test-suite/failure/guard.v b/test-suite/failure/guard.v
new file mode 100644
index 00000000..46208c29
--- /dev/null
+++ b/test-suite/failure/guard.v
@@ -0,0 +1,10 @@
+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(************************************************************************)
+
+Fixpoint F (n:nat) : False := F (match F n with end).
+
diff --git a/test-suite/failure/rewrite_in_hyp2.v b/test-suite/failure/rewrite_in_hyp2.v
new file mode 100644
index 00000000..a32037a2
--- /dev/null
+++ b/test-suite/failure/rewrite_in_hyp2.v
@@ -0,0 +1,8 @@
+(* Until revision 10221, rewriting in hypotheses of the form
+ "(fun x => phi(x)) t" with "t" not rewritable used to behave as a
+ beta-normalization tactic instead of raising the expected message
+ "nothing to rewrite" *)
+
+Goal forall b, S b = O -> (fun a => 0 = (S a)) b -> True.
+ intros b H H0.
+ rewrite H in H0.
diff --git a/test-suite/failure/subtyping.v b/test-suite/failure/subtyping.v
new file mode 100644
index 00000000..35fd2036
--- /dev/null
+++ b/test-suite/failure/subtyping.v
@@ -0,0 +1,21 @@
+(* A variant of bug #1302 that must fail *)
+
+Module Type T.
+
+ Parameter A : Type.
+
+ Inductive L : Prop :=
+ | L0
+ | L1 : (A -> Prop) -> L.
+
+End T.
+
+Module TT : T.
+
+ Parameter A : Type.
+
+ Inductive L : Type :=
+ | L0
+ | L1 : (A -> Prop) -> L.
+
+End TT.
diff --git a/test-suite/failure/subtyping2.v b/test-suite/failure/subtyping2.v
new file mode 100644
index 00000000..0a75ae45
--- /dev/null
+++ b/test-suite/failure/subtyping2.v
@@ -0,0 +1,245 @@
+(* Check that no constraints on inductive types disappear at subtyping *)
+
+Module Type S.
+
+Record A0 : Type := (* Type_i' *)
+ i0 {X0 : Type; R0 : X0 -> X0 -> Prop}. (* X0: Type_j' *)
+
+Variable i0' : forall X0 : Type, (X0 -> X0 -> Prop) -> A0.
+
+End S.
+
+Module M.
+
+Record A0 : Type := (* Type_i' *)
+ i0 {X0 : Type; R0 : X0 -> X0 -> Prop}. (* X0: Type_j' *)
+
+Definition i0' := i0 : forall X0 : Type, (X0 -> X0 -> Prop) -> A0.
+
+End M.
+
+(* The rest of this file formalizes Burali-Forti paradox *)
+(* (if the constraint between i0' and A0 is lost, the proof goes through) *)
+
+ Inductive ACC (A : Type) (R : A -> A -> Prop) : A -> Prop :=
+ ACC_intro :
+ forall x : A, (forall y : A, R y x -> ACC A R y) -> ACC A R x.
+
+ Lemma ACC_nonreflexive :
+ forall (A : Type) (R : A -> A -> Prop) (x : A),
+ ACC A R x -> R x x -> False.
+simple induction 1; intros.
+exact (H1 x0 H2 H2).
+Qed.
+
+ Definition WF (A : Type) (R : A -> A -> Prop) := forall x : A, ACC A R x.
+
+
+Section Inverse_Image.
+
+ Variables (A B : Type) (R : B -> B -> Prop) (f : A -> B).
+
+ Definition Rof (x y : A) : Prop := R (f x) (f y).
+
+ Remark ACC_lemma :
+ forall y : B, ACC B R y -> forall x : A, y = f x -> ACC A Rof x.
+ simple induction 1; intros.
+ constructor; intros.
+ apply (H1 (f y0)); trivial.
+ elim H2 using eq_ind_r; trivial.
+ Qed.
+
+ Lemma ACC_inverse_image : forall x : A, ACC B R (f x) -> ACC A Rof x.
+ intros; apply (ACC_lemma (f x)); trivial.
+ Qed.
+
+ Lemma WF_inverse_image : WF B R -> WF A Rof.
+ red in |- *; intros; apply ACC_inverse_image; auto.
+ Qed.
+
+End Inverse_Image.
+
+Section Burali_Forti_Paradox.
+
+ Definition morphism (A : Type) (R : A -> A -> Prop)
+ (B : Type) (S : B -> B -> Prop) (f : A -> B) :=
+ forall x y : A, R x y -> S (f x) (f y).
+
+ (* The hypothesis of the paradox:
+ assumes there exists an universal system of notations, i.e:
+ - A type A0
+ - An injection i0 from relations on any type into A0
+ - The proof that i0 is injective modulo morphism
+ *)
+ Variable A0 : Type. (* Type_i *)
+ Variable i0 : forall X : Type, (X -> X -> Prop) -> A0. (* X: Type_j *)
+ Hypothesis
+ inj :
+ forall (X1 : Type) (R1 : X1 -> X1 -> Prop) (X2 : Type)
+ (R2 : X2 -> X2 -> Prop),
+ i0 X1 R1 = i0 X2 R2 -> exists f : X1 -> X2, morphism X1 R1 X2 R2 f.
+
+ (* Embedding of x in y: x and y are images of 2 well founded relations
+ R1 and R2, the ordinal of R2 being strictly greater than that of R1.
+ *)
+ Record emb (x y : A0) : Prop :=
+ {X1 : Type;
+ R1 : X1 -> X1 -> Prop;
+ eqx : x = i0 X1 R1;
+ X2 : Type;
+ R2 : X2 -> X2 -> Prop;
+ eqy : y = i0 X2 R2;
+ W2 : WF X2 R2;
+ f : X1 -> X2;
+ fmorph : morphism X1 R1 X2 R2 f;
+ maj : X2;
+ majf : forall z : X1, R2 (f z) maj}.
+
+
+ Lemma emb_trans : forall x y z : A0, emb x y -> emb y z -> emb x z.
+intros.
+case H; intros.
+case H0; intros.
+generalize eqx0; clear eqx0.
+elim eqy using eq_ind_r; intro.
+case (inj _ _ _ _ eqx0); intros.
+exists X1 R1 X3 R3 (fun x : X1 => f0 (x0 (f x))) maj0; trivial.
+red in |- *; auto.
+Defined.
+
+
+ Lemma ACC_emb :
+ forall (X : Type) (R : X -> X -> Prop) (x : X),
+ ACC X R x ->
+ forall (Y : Type) (S : Y -> Y -> Prop) (f : Y -> X),
+ morphism Y S X R f -> (forall y : Y, R (f y) x) -> ACC A0 emb (i0 Y S).
+simple induction 1; intros.
+constructor; intros.
+case H4; intros.
+elim eqx using eq_ind_r.
+case (inj X2 R2 Y S).
+apply sym_eq; assumption.
+
+intros.
+apply H1 with (y := f (x1 maj)) (f := fun x : X1 => f (x1 (f0 x)));
+ try red in |- *; auto.
+Defined.
+
+ (* The embedding relation is well founded *)
+ Lemma WF_emb : WF A0 emb.
+constructor; intros.
+case H; intros.
+elim eqx using eq_ind_r.
+apply ACC_emb with (X := X2) (R := R2) (x := maj) (f := f); trivial.
+Defined.
+
+
+ (* The following definition enforces Type_j >= Type_i *)
+ Definition Omega : A0 := i0 A0 emb.
+
+
+Section Subsets.
+
+ Variable a : A0.
+
+ (* We define the type of elements of A0 smaller than a w.r.t embedding.
+ The Record is in Type, but it is possible to avoid such structure. *)
+ Record sub : Type := {witness : A0; emb_wit : emb witness a}.
+
+ (* F is its image through i0 *)
+ Definition F : A0 := i0 sub (Rof _ _ emb witness).
+
+ (* F is embedded in Omega:
+ - the witness projection is a morphism
+ - a is an upper bound because emb_wit proves that witness is
+ smaller than a.
+ *)
+ Lemma F_emb_Omega : emb F Omega.
+exists sub (Rof _ _ emb witness) A0 emb witness a; trivial.
+exact WF_emb.
+
+red in |- *; trivial.
+
+exact emb_wit.
+Defined.
+
+End Subsets.
+
+
+ Definition fsub (a b : A0) (H : emb a b) (x : sub a) :
+ sub b := Build_sub _ (witness _ x) (emb_trans _ _ _ (emb_wit _ x) H).
+
+ (* F is a morphism: a < b => F(a) < F(b)
+ - the morphism from F(a) to F(b) is fsub above
+ - the upper bound is a, which is in F(b) since a < b
+ *)
+ Lemma F_morphism : morphism A0 emb A0 emb F.
+red in |- *; intros.
+exists
+ (sub x)
+ (Rof _ _ emb (witness x))
+ (sub y)
+ (Rof _ _ emb (witness y))
+ (fsub x y H)
+ (Build_sub _ x H); trivial.
+apply WF_inverse_image.
+exact WF_emb.
+
+unfold morphism, Rof, fsub in |- *; simpl in |- *; intros.
+trivial.
+
+unfold Rof, fsub in |- *; simpl in |- *; intros.
+apply emb_wit.
+Defined.
+
+
+ (* Omega is embedded in itself:
+ - F is a morphism
+ - Omega is an upper bound of the image of F
+ *)
+ Lemma Omega_refl : emb Omega Omega.
+exists A0 emb A0 emb F Omega; trivial.
+exact WF_emb.
+
+exact F_morphism.
+
+exact F_emb_Omega.
+Defined.
+
+ (* The paradox is that Omega cannot be embedded in itself, since
+ the embedding relation is well founded.
+ *)
+ Theorem Burali_Forti : False.
+apply ACC_nonreflexive with A0 emb Omega.
+apply WF_emb.
+
+exact Omega_refl.
+
+Defined.
+
+End Burali_Forti_Paradox.
+
+Import M.
+
+ (* Note: this proof uses a large elimination of A0. *)
+ Lemma inj :
+ forall (X1 : Type) (R1 : X1 -> X1 -> Prop) (X2 : Type)
+ (R2 : X2 -> X2 -> Prop),
+ i0' X1 R1 = i0' X2 R2 -> exists f : X1 -> X2, morphism X1 R1 X2 R2 f.
+intros.
+change
+ match i0' X1 R1, i0' X2 R2 with
+ | i0 x1 r1, i0 x2 r2 => exists f : _, morphism x1 r1 x2 r2 f
+ end in |- *.
+case H; simpl in |- *.
+exists (fun x : X1 => x).
+red in |- *; trivial.
+Defined.
+
+(* The following command raises 'Error: Universe Inconsistency'.
+ To allow large elimination of A0, i0 must not be a large constructor.
+ Hence, the constraint Type_j' < Type_i' is added, which is incompatible
+ with the constraint j >= i in the paradox.
+*)
+
+ Definition Paradox : False := Burali_Forti A0 i0' inj.
diff --git a/test-suite/failure/univ_include.v b/test-suite/failure/univ_include.v
new file mode 100644
index 00000000..4be70d88
--- /dev/null
+++ b/test-suite/failure/univ_include.v
@@ -0,0 +1,30 @@
+Definition T := Type.
+Definition U := Type.
+
+Module Type MT.
+ Parameter t : T.
+End MT.
+
+Module Type MU.
+ Parameter t : U.
+End MU.
+
+Module F (E : MT).
+ Definition elt :T := E.t.
+End F.
+
+Module G (E : MU).
+ Include F E.
+Print Universes. (* U <= T *)
+End G.
+Print Universes. (* Check if constraint is lost *)
+
+Module Mt.
+ Definition t := T.
+End Mt.
+
+Module P := G Mt. (* should yield Universe inconsistency *)
+(* ... otherwise the following command will show that T has type T! *)
+Eval cbv delta [P.elt Mt.t] in P.elt.
+
+
diff --git a/test-suite/ide/undo.v b/test-suite/ide/undo.v
new file mode 100644
index 00000000..60c2e657
--- /dev/null
+++ b/test-suite/ide/undo.v
@@ -0,0 +1,79 @@
+(* Here are a sequences of scripts to test interactively with undo and
+ replay in coqide proof sessions *)
+
+(* Undoing arbitrary commands, as first step *)
+
+Theorem a : O=O.
+Ltac f x := x.
+assert True by trivial.
+trivial.
+Qed.
+
+(* Undoing arbitrary commands, as non-first step *)
+
+Theorem b : O=O.
+assert True by trivial.
+Ltac g x := x.
+assert True by trivial.
+trivial.
+Qed.
+
+(* Undoing declarations, as first step *)
+(* was bugged in 8.1 *)
+
+Theorem c : O=O.
+Inductive T : Type := I.
+trivial.
+Qed.
+
+(* Undoing declarations, as first step *)
+(* new in 8.2 *)
+
+Theorem d : O=O.
+Definition e := O.
+Definition f := O.
+assert True by trivial.
+trivial.
+Qed.
+
+(* Undoing declarations, as non-first step *)
+(* new in 8.2 *)
+
+Theorem h : O=O.
+assert True by trivial.
+Definition i := O.
+Definition j := O.
+assert True by trivial.
+trivial.
+Qed.
+
+(* Undoing declarations, interleaved with proof steps *)
+(* new in 8.2 *)
+
+Theorem k : O=O.
+assert True by trivial.
+Definition l := O.
+assert True by trivial.
+Definition m := O.
+assert True by trivial.
+trivial.
+Qed.
+
+(* Undoing declarations, interleaved with proof steps and commands *)
+(* new in 8.2 *)
+
+Theorem n : O=O.
+assert True by trivial.
+Definition o := O.
+Ltac h x := x.
+assert True by trivial.
+Focus.
+Definition p := O.
+assert True by trivial.
+trivial.
+Qed.
+
+(* Undoing declarations, not in proof *)
+
+Definition q := O.
+Definition r := O.
diff --git a/test-suite/ideal-features/Case9.v b/test-suite/ideal-features/Case9.v
new file mode 100644
index 00000000..800c431e
--- /dev/null
+++ b/test-suite/ideal-features/Case9.v
@@ -0,0 +1,12 @@
+(* Exemple soumis par Pierre Corbineau (bug #1671) *)
+
+CoInductive hdlist : unit -> Type :=
+| cons : hdlist tt -> hdlist tt.
+
+Variable P : forall bo, hdlist bo -> Prop.
+Variable all : forall bo l, P bo l.
+
+Definition F (l:hdlist tt) : P tt l :=
+match l in hdlist u return P u l with
+| cons (cons l') => all tt _
+end.
diff --git a/test-suite/ideal-features/complexity/evars_subst.v b/test-suite/ideal-features/complexity/evars_subst.v
new file mode 100644
index 00000000..6f9f86a9
--- /dev/null
+++ b/test-suite/ideal-features/complexity/evars_subst.v
@@ -0,0 +1,53 @@
+(* Bug report #932 *)
+(* Expected time < 1.00s *)
+
+(* Let n be the number of let-in. The complexity comes from the fact
+ that each implicit arguments of f was in a larger and larger
+ context. To compute the type of "let _ := f ?Tn 0 in f ?T 0",
+ "f ?Tn 0" is substituted in the type of "f ?T 0" which is ?T. This
+ type is an evar instantiated on the n variables denoting the "f ?Ti 0".
+ One obtain "?T[1;...;n-1;f ?Tn[1;...;n-1] 0]". To compute the
+ type of "let _ := f ?Tn-1 0 in let _ := f ?Tn 0 in f ?T 0", another
+ substitution is done leading to
+ "?T[1;...;n-2;f ?Tn[1;...;n-2] 0;f ?Tn[1;...;n-2;f ?Tn[1;...;n-2] 0] 0]"
+ and so on. At the end, we get a term of exponential size *)
+
+(* A way to cut the complexity could have been to remove the dependency in
+ anonymous variables in evars but this breaks intuitive behaviour
+ (see Case15.v); another approach could be to substitute lazily
+ and/or to simultaneously substitute let binders and evars *)
+
+Variable P : Set -> Set.
+Variable f : forall A : Set, A -> P A.
+
+Time Check
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+
+ f _ 0.
+
diff --git a/test-suite/ideal-features/evars_subst.v b/test-suite/ideal-features/evars_subst.v
new file mode 100644
index 00000000..6f9f86a9
--- /dev/null
+++ b/test-suite/ideal-features/evars_subst.v
@@ -0,0 +1,53 @@
+(* Bug report #932 *)
+(* Expected time < 1.00s *)
+
+(* Let n be the number of let-in. The complexity comes from the fact
+ that each implicit arguments of f was in a larger and larger
+ context. To compute the type of "let _ := f ?Tn 0 in f ?T 0",
+ "f ?Tn 0" is substituted in the type of "f ?T 0" which is ?T. This
+ type is an evar instantiated on the n variables denoting the "f ?Ti 0".
+ One obtain "?T[1;...;n-1;f ?Tn[1;...;n-1] 0]". To compute the
+ type of "let _ := f ?Tn-1 0 in let _ := f ?Tn 0 in f ?T 0", another
+ substitution is done leading to
+ "?T[1;...;n-2;f ?Tn[1;...;n-2] 0;f ?Tn[1;...;n-2;f ?Tn[1;...;n-2] 0] 0]"
+ and so on. At the end, we get a term of exponential size *)
+
+(* A way to cut the complexity could have been to remove the dependency in
+ anonymous variables in evars but this breaks intuitive behaviour
+ (see Case15.v); another approach could be to substitute lazily
+ and/or to simultaneously substitute let binders and evars *)
+
+Variable P : Set -> Set.
+Variable f : forall A : Set, A -> P A.
+
+Time Check
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+ let _ := f _ 0 in
+
+ f _ 0.
+
diff --git a/test-suite/ideal-features/universes.v b/test-suite/ideal-features/universes.v
new file mode 100644
index 00000000..6db4cfe1
--- /dev/null
+++ b/test-suite/ideal-features/universes.v
@@ -0,0 +1,43 @@
+(* Some issues with polymorphic inductive types *)
+
+(* 1- upper constraints with respect to non polymorphic inductive types *)
+
+Unset Elimination Schemes.
+Definition Ty := Type (* Top.1 *).
+
+Inductive Q (A:Type (* Top.2 *)) : Prop := q : A -> Q A.
+Inductive T (B:Type (* Top.3 *)) := t : B -> Q (T B) -> T B.
+(* ajoute Top.4 <= Top.2 inutilement:
+ 4 est l'univers utilisé dans le calcul du type polymorphe de T *)
+Definition C := T Ty.
+(* ajoute Top.1 < Top.3 :
+ Top.3 jour le rôle de pivot pour propager les contraintes supérieures qu'on
+ a sur l'argument B de T: Top.3 sera réutilisé plus tard comme majorant
+ des arguments effectifs de T, propageant à cette occasion les contraintes
+ supérieures sur Top.3 *)
+
+(* We need either that Q is polymorphic on A (though it is in Type) or
+ that the constraint Top.1 < Top.2 is set (and it is not set!) *)
+
+(* 2- upper constraints with respect to unfoldable constants *)
+
+Definition f (A:Type (* Top.1 *)) := True.
+Inductive R := r : f R -> R.
+(* ajoute Top.3 <= Top.1 inutilement:
+ Top.3 est l'univers utilisé dans le calcul du type polymorphe de R *)
+
+(* mais il manque la contrainte que l'univers de R est plus petit que Top.1
+ ce qui l'empêcherait en fait d'être vraiment polymorphe *)
+
+(* 3- constraints with respect to global constants *)
+
+Inductive S (A:Ty) := s : A -> S A.
+
+(* Q est considéré polymorphique vis à vis de A alors que le type de A
+ n'est pas une variable mais un univers déjà existant *)
+
+(* Malgré tout la contrainte Ty < Ty est ajoutée (car Ty est vu comme
+ un pivot pour propager les contraintes sur le type A, comme si Q était
+ vraiment polymorphique, ce qu'il n'est pas parce que Ty est une
+ constante). Et heureusement qu'elle est ajouté car elle évite de
+ pouvoir typer "Q Ty" *)
diff --git a/test-suite/micromega/bertot.v b/test-suite/micromega/bertot.v
new file mode 100644
index 00000000..6951fcd3
--- /dev/null
+++ b/test-suite/micromega/bertot.v
@@ -0,0 +1,22 @@
+(************************************************************************)
+(* *)
+(* Micromega: A reflexive tactic using the Positivstellensatz *)
+(* *)
+(* Frédéric Besson (Irisa/Inria) 2006-2008 *)
+(* *)
+(************************************************************************)
+
+Require Import ZArith.
+Require Import Micromegatac.
+
+Open Scope Z_scope.
+
+Goal (forall x y n,
+ ( ~ x < n /\ x <= n /\ 2 * y = x*(x+1) -> 2 * y = n*(n+1))
+ /\
+ (x < n /\ x <= n /\ 2 * y = x * (x+1) -> x + 1 <= n /\ 2 *(x+1+y) = (x+1)*(x+2))).
+Proof.
+ intros.
+ micromega Z.
+Qed.
+
diff --git a/test-suite/micromega/example.v b/test-suite/micromega/example.v
new file mode 100644
index 00000000..dc78ace5
--- /dev/null
+++ b/test-suite/micromega/example.v
@@ -0,0 +1,347 @@
+(************************************************************************)
+(* *)
+(* Micromega: A reflexive tactic using the Positivstellensatz *)
+(* *)
+(* Frédéric Besson (Irisa/Inria) 2006-2008 *)
+(* *)
+(************************************************************************)
+
+Require Import ZArith.
+Require Import Micromegatac.
+Require Import Ring_normalize.
+Open Scope Z_scope.
+Require Import ZMicromega.
+Require Import VarMap.
+
+(* false in Q : x=1/2 and n=1 *)
+
+Lemma not_so_easy : forall x n : Z,
+ 2*x + 1 <= 2 *n -> x <= n-1.
+Proof.
+ intros.
+ zfarkas.
+Qed.
+
+
+(* From Laurent Théry *)
+
+Lemma some_pol : forall x, 4 * x ^ 2 + 3 * x + 2 >= 0.
+Proof.
+ intros.
+ micromega Z.
+Qed.
+
+
+Lemma Zdiscr: forall a b c x,
+ a * x ^ 2 + b * x + c = 0 -> b ^ 2 - 4 * a * c >= 0.
+Proof.
+ intros ; micromega Z.
+Qed.
+
+
+Lemma plus_minus : forall x y,
+ 0 = x + y -> 0 = x -y -> 0 = x /\ 0 = y.
+Proof.
+ intros.
+ zfarkas.
+Qed.
+
+
+
+Lemma mplus_minus : forall x y,
+ x + y >= 0 -> x -y >= 0 -> x^2 - y^2 >= 0.
+Proof.
+ intros; micromega Z.
+Qed.
+
+Lemma pol3: forall x y, 0 <= x + y ->
+ x^3 + 3*x^2*y + 3*x* y^2 + y^3 >= 0.
+Proof.
+ intros; micromega Z.
+Qed.
+
+
+(* Motivating example from: Expressiveness + Automation + Soundness:
+ Towards COmbining SMT Solvers and Interactive Proof Assistants *)
+Parameter rho : Z.
+Parameter rho_ge : rho >= 0.
+Parameter correct : Z -> Z -> Prop.
+
+
+Definition rbound1 (C:Z -> Z -> Z) : Prop :=
+ forall p s t, correct p t /\ s <= t -> C p t - C p s <= (1-rho)*(t-s).
+
+Definition rbound2 (C:Z -> Z -> Z) : Prop :=
+ forall p s t, correct p t /\ s <= t -> (1-rho)*(t-s) <= C p t - C p s.
+
+
+Lemma bounded_drift : forall s t p q C D, s <= t /\ correct p t /\ correct q t /\
+ rbound1 C /\ rbound2 C /\ rbound1 D /\ rbound2 D ->
+ Zabs (C p t - D q t) <= Zabs (C p s - D q s) + 2 * rho * (t- s).
+Proof.
+ intros.
+ generalize (Zabs_eq (C p t - D q t)).
+ generalize (Zabs_non_eq (C p t - D q t)).
+ generalize (Zabs_eq (C p s -D q s)).
+ generalize (Zabs_non_eq (C p s - D q s)).
+ unfold rbound2 in H.
+ unfold rbound1 in H.
+ intuition.
+ generalize (H6 _ _ _ (conj H H4)).
+ generalize (H7 _ _ _ (conj H H4)).
+ generalize (H8 _ _ _ (conj H H4)).
+ generalize (H10 _ _ _ (conj H H4)).
+ generalize (H6 _ _ _ (conj H5 H4)).
+ generalize (H7 _ _ _ (conj H5 H4)).
+ generalize (H8 _ _ _ (conj H5 H4)).
+ generalize (H10 _ _ _ (conj H5 H4)).
+ generalize rho_ge.
+ micromega Z.
+Qed.
+
+(* Rule of signs *)
+
+Lemma sign_pos_pos: forall x y,
+ x > 0 -> y > 0 -> x*y > 0.
+Proof.
+ intros; micromega Z.
+Qed.
+
+Lemma sign_pos_zero: forall x y,
+ x > 0 -> y = 0 -> x*y = 0.
+Proof.
+ intros; micromega Z.
+Qed.
+
+Lemma sign_pos_neg: forall x y,
+ x > 0 -> y < 0 -> x*y < 0.
+Proof.
+ intros; micromega Z.
+Qed.
+
+Lemma sign_zer_pos: forall x y,
+ x = 0 -> y > 0 -> x*y = 0.
+Proof.
+ intros; micromega Z.
+Qed.
+
+Lemma sign_zero_zero: forall x y,
+ x = 0 -> y = 0 -> x*y = 0.
+Proof.
+ intros; micromega Z.
+Qed.
+
+Lemma sign_zero_neg: forall x y,
+ x = 0 -> y < 0 -> x*y = 0.
+Proof.
+ intros; micromega Z.
+Qed.
+
+Lemma sign_neg_pos: forall x y,
+ x < 0 -> y > 0 -> x*y < 0.
+Proof.
+ intros; micromega Z.
+Qed.
+
+Lemma sign_neg_zero: forall x y,
+ x < 0 -> y = 0 -> x*y = 0.
+Proof.
+ intros; micromega Z.
+Qed.
+
+Lemma sign_neg_neg: forall x y,
+ x < 0 -> y < 0 -> x*y > 0.
+Proof.
+ intros; micromega Z.
+Qed.
+
+
+(* Other (simple) examples *)
+
+Lemma binomial : forall x y, (x+y)^2 = x^2 + 2*x*y + y^2.
+Proof.
+ intros.
+ zfarkas.
+Qed.
+
+Lemma product : forall x y, x >= 0 -> y >= 0 -> x * y >= 0.
+Proof.
+ intros.
+ micromega Z.
+Qed.
+
+
+Lemma product_strict : forall x y, x > 0 -> y > 0 -> x * y > 0.
+Proof.
+ intros.
+ micromega Z.
+Qed.
+
+
+Lemma pow_2_pos : forall x, x ^ 2 + 1 = 0 -> False.
+Proof.
+ intros ; micromega Z.
+Qed.
+
+(* Found in Parrilo's talk *)
+(* BUG?: certificate with **very** big coefficients *)
+Lemma parrilo_ex : forall x y, x - y^2 + 3 >= 0 -> y + x^2 + 2 = 0 -> False.
+Proof.
+ intros.
+ micromega Z.
+Qed.
+
+
+(* from hol_light/Examples/sos.ml *)
+
+Lemma hol_light1 : forall a1 a2 b1 b2,
+ a1 >= 0 -> a2 >= 0 ->
+ (a1 * a1 + a2 * a2 = b1 * b1 + b2 * b2 + 2) ->
+ (a1 * b1 + a2 * b2 = 0) -> a1 * a2 - b1 * b2 >= 0.
+Proof.
+ intros ; micromega Z.
+Qed.
+
+
+Lemma hol_light2 : forall x a,
+ 3 * x + 7 * a < 4 -> 3 < 2 * x -> a < 0.
+Proof.
+ intros ; micromega Z.
+Qed.
+
+Lemma hol_light3 : forall b a c x,
+ b ^ 2 < 4 * a * c -> (a * x ^2 + b * x + c = 0) -> False.
+Proof.
+intros ; micromega Z.
+Qed.
+
+Lemma hol_light4 : forall a c b x,
+ a * x ^ 2 + b * x + c = 0 -> b ^ 2 >= 4 * a * c.
+Proof.
+intros ; micromega Z.
+Qed.
+
+Lemma hol_light5 : forall x y,
+ 0 <= x /\ x <= 1 /\ 0 <= y /\ y <= 1
+ -> x ^ 2 + y ^ 2 < 1 \/
+ (x - 1) ^ 2 + y ^ 2 < 1 \/
+ x ^ 2 + (y - 1) ^ 2 < 1 \/
+ (x - 1) ^ 2 + (y - 1) ^ 2 < 1.
+Proof.
+intros; micromega Z.
+Qed.
+
+
+
+Lemma hol_light7 : forall x y z,
+ 0<= x /\ 0 <= y /\ 0 <= z /\ x + y + z <= 3
+ -> x * y + x * z + y * z >= 3 * x * y * z.
+Proof.
+intros ; micromega Z.
+Qed.
+
+Lemma hol_light8 : forall x y z,
+ x ^ 2 + y ^ 2 + z ^ 2 = 1 -> (x + y + z) ^ 2 <= 3.
+Proof.
+ intros ; micromega Z.
+Qed.
+
+Lemma hol_light9 : forall w x y z,
+ w ^ 2 + x ^ 2 + y ^ 2 + z ^ 2 = 1
+ -> (w + x + y + z) ^ 2 <= 4.
+Proof.
+ intros;micromega Z.
+Qed.
+
+Lemma hol_light10 : forall x y,
+ x >= 1 /\ y >= 1 -> x * y >= x + y - 1.
+Proof.
+ intros ; micromega Z.
+Qed.
+
+Lemma hol_light11 : forall x y,
+ x > 1 /\ y > 1 -> x * y > x + y - 1.
+Proof.
+ intros ; micromega Z.
+Qed.
+
+
+Lemma hol_light12: forall x y z,
+ 2 <= x /\ x <= 125841 / 50000 /\
+ 2 <= y /\ y <= 125841 / 50000 /\
+ 2 <= z /\ z <= 125841 / 50000
+ -> 2 * (x * z + x * y + y * z) - (x * x + y * y + z * z) >= 0.
+Proof.
+ intros x y z ; set (e:= (125841 / 50000)).
+ compute in e.
+ unfold e ; intros ; micromega Z.
+Qed.
+
+Lemma hol_light14 : forall x y z,
+ 2 <= x /\ x <= 4 /\ 2 <= y /\ y <= 4 /\ 2 <= z /\ z <= 4
+ -> 12 <= 2 * (x * z + x * y + y * z) - (x * x + y * y + z * z).
+Proof.
+ intros ;micromega Z.
+Qed.
+
+(* ------------------------------------------------------------------------- *)
+(* Inequality from sci.math (see "Leon-Sotelo, por favor"). *)
+(* ------------------------------------------------------------------------- *)
+
+Lemma hol_light16 : forall x y,
+ 0 <= x /\ 0 <= y /\ (x * y = 1)
+ -> x + y <= x ^ 2 + y ^ 2.
+Proof.
+ intros ; micromega Z.
+Qed.
+
+Lemma hol_light17 : forall x y,
+ 0 <= x /\ 0 <= y /\ (x * y = 1)
+ -> x * y * (x + y) <= x ^ 2 + y ^ 2.
+Proof.
+ intros ; micromega Z.
+Qed.
+
+Lemma hol_light18 : forall x y,
+ 0 <= x /\ 0 <= y -> x * y * (x + y) ^ 2 <= (x ^ 2 + y ^ 2) ^ 2.
+Proof.
+ intros ; micromega Z.
+Qed.
+
+(* ------------------------------------------------------------------------- *)
+(* Some examples over integers and natural numbers. *)
+(* ------------------------------------------------------------------------- *)
+
+Lemma hol_light19 : forall m n, 2 * m + n = (n + m) + m.
+Proof.
+ intros ; zfarkas.
+Qed.
+
+Lemma hol_light22 : forall n, n >= 0 -> n <= n * n.
+Proof.
+ intros.
+ micromega Z.
+Qed.
+
+
+Lemma hol_light24 : forall x1 y1 x2 y2, x1 >= 0 -> x2 >= 0 -> y1 >= 0 -> y2 >= 0 ->
+ ((x1 + y1) ^2 + x1 + 1 = (x2 + y2) ^ 2 + x2 + 1)
+ -> (x1 + y1 = x2 + y2).
+Proof.
+ intros.
+ micromega Z.
+Qed.
+
+Lemma motzkin' : forall x y, (x^2+y^2+1)*(x^2*y^4 + x^4*y^2 + 1 - 3*x^2*y^2) >= 0.
+Proof.
+ intros ; sos Z.
+Qed.
+
+
+
+Lemma motzkin : forall x y, (x^2*y^4 + x^4*y^2 + 1 - 3*x^2*y^2) >= 0.
+Proof.
+ intros.
+ generalize (motzkin' x y).
+ micromega Z.
+Qed.
diff --git a/test-suite/micromega/heap3_vcgen_25.v b/test-suite/micromega/heap3_vcgen_25.v
new file mode 100644
index 00000000..ec88b68d
--- /dev/null
+++ b/test-suite/micromega/heap3_vcgen_25.v
@@ -0,0 +1,38 @@
+(************************************************************************)
+(* *)
+(* Micromega: A reflexive tactic using the Positivstellensatz *)
+(* *)
+(* Frédéric Besson (Irisa/Inria) 2006-2008 *)
+(* *)
+(************************************************************************)
+
+Require Import ZArith.
+Require Import Micromegatac.
+
+Open Scope Z_scope.
+
+Lemma vcgen_25 : forall
+ (n : Z)
+ (m : Z)
+ (jt : Z)
+ (j : Z)
+ (it : Z)
+ (i : Z)
+ (H0 : 1 * it + -2 * i + -1 = 0)
+ (H : 1 * jt + -2 * j + -1 = 0)
+ (H1 : 1 * n + -10 = 0)
+ (H2 : 0 <= -4028 * i + 6222 * j + 705 * m + -16674)
+ (H3 : 0 <= -418 * i + 651 * j + 94 * m + -1866)
+ (H4 : 0 <= -209 * i + 302 * j + 47 * m + -839)
+ (H5 : 0 <= -1 * i + 1 * j + -1)
+ (H6 : 0 <= -1 * j + 1 * m + 0)
+ (H7 : 0 <= 1 * j + 5 * m + -27)
+ (H8 : 0 <= 2 * j + -1 * m + 2)
+ (H9 : 0 <= 7 * j + 10 * m + -74)
+ (H10 : 0 <= 18 * j + -139 * m + 1188)
+ (H11 : 0 <= 1 * i + 0)
+ (H13 : 0 <= 121 * i + 810 * j + -7465 * m + 64350),
+ (1 = -2 * i + it).
+Proof.
+ intros ; zfarkas.
+Qed.
diff --git a/test-suite/micromega/qexample.v b/test-suite/micromega/qexample.v
new file mode 100644
index 00000000..42aff5a4
--- /dev/null
+++ b/test-suite/micromega/qexample.v
@@ -0,0 +1,62 @@
+(************************************************************************)
+(* *)
+(* Micromega: A reflexive tactic using the Positivstellensatz *)
+(* *)
+(* Frédéric Besson (Irisa/Inria) 2006-2008 *)
+(* *)
+(************************************************************************)
+
+Require Import Micromegatac.
+Require Import QArith.
+Require Import Ring_normalize.
+
+Lemma plus_minus : forall x y,
+ 0 == x + y -> 0 == x -y -> 0 == x /\ 0 == y.
+Proof.
+ intros.
+ omicron Q.
+Qed.
+
+(* Other (simple) examples *)
+Open Scope Q_scope.
+
+Lemma binomial : forall x y:Q, ((x+y)^2 == x^2 + (2 # 1) *x*y + y^2).
+Proof.
+ intros.
+ omicron Q.
+Qed.
+
+
+Lemma hol_light19 : forall m n, (2 # 1) * m + n == (n + m) + m.
+Proof.
+ intros ; omicron Q.
+Qed.
+Open Scope Z_scope.
+Open Scope Q_scope.
+
+Lemma vcgen_25 : forall
+ (n : Q)
+ (m : Q)
+ (jt : Q)
+ (j : Q)
+ (it : Q)
+ (i : Q)
+ (H0 : 1 * it + (-2 # 1) * i + (-1 # 1) == 0)
+ (H : 1 * jt + (-2 # 1) * j + (-1 # 1) == 0)
+ (H1 : 1 * n + (-10 # 1) = 0)
+ (H2 : 0 <= (-4028 # 1) * i + (6222 # 1) * j + (705 # 1) * m + (-16674 # 1))
+ (H3 : 0 <= (-418 # 1) * i + (651 # 1) * j + (94 # 1) * m + (-1866 # 1))
+ (H4 : 0 <= (-209 # 1) * i + (302 # 1) * j + (47 # 1) * m + (-839 # 1))
+ (H5 : 0 <= (-1 # 1) * i + 1 * j + (-1 # 1))
+ (H6 : 0 <= (-1 # 1) * j + 1 * m + (0 # 1))
+ (H7 : 0 <= (1 # 1) * j + (5 # 1) * m + (-27 # 1))
+ (H8 : 0 <= (2 # 1) * j + (-1 # 1) * m + (2 # 1))
+ (H9 : 0 <= (7 # 1) * j + (10 # 1) * m + (-74 # 1))
+ (H10 : 0 <= (18 # 1) * j + (-139 # 1) * m + (1188 # 1))
+ (H11 : 0 <= 1 * i + (0 # 1))
+ (H13 : 0 <= (121 # 1) * i + (810 # 1) * j + (-7465 # 1) * m + (64350 # 1)),
+ (( 1# 1) == (-2 # 1) * i + it).
+Proof.
+ intros.
+ omicron Q.
+Qed.
diff --git a/test-suite/micromega/rexample.v b/test-suite/micromega/rexample.v
new file mode 100644
index 00000000..5132dc4e
--- /dev/null
+++ b/test-suite/micromega/rexample.v
@@ -0,0 +1,62 @@
+(************************************************************************)
+(* *)
+(* Micromega: A reflexive tactic using the Positivstellensatz *)
+(* *)
+(* Frédéric Besson (Irisa/Inria) 2006-2008 *)
+(* *)
+(************************************************************************)
+
+Require Import Micromegatac.
+Require Import Reals.
+Require Import Ring_normalize.
+
+Open Scope R_scope.
+
+Lemma plus_minus : forall x y,
+ 0 = x + y -> 0 = x -y -> 0 = x /\ 0 = y.
+Proof.
+ intros.
+ omicron R.
+Qed.
+
+(* Other (simple) examples *)
+
+Lemma binomial : forall x y, ((x+y)^2 = x^2 + 2 *x*y + y^2).
+Proof.
+ intros.
+ omicron R.
+Qed.
+
+
+Lemma hol_light19 : forall m n, 2 * m + n = (n + m) + m.
+Proof.
+ intros ; omicron R.
+Qed.
+
+
+Lemma vcgen_25 : forall
+ (n : R)
+ (m : R)
+ (jt : R)
+ (j : R)
+ (it : R)
+ (i : R)
+ (H0 : 1 * it + (-2%R ) * i + (-1%R ) = 0)
+ (H : 1 * jt + (-2 ) * j + (-1 ) = 0)
+ (H1 : 1 * n + (-10 ) = 0)
+ (H2 : 0 <= (-4028 ) * i + (6222 ) * j + (705 ) * m + (-16674 ))
+ (H3 : 0 <= (-418 ) * i + (651 ) * j + (94 ) * m + (-1866 ))
+ (H4 : 0 <= (-209 ) * i + (302 ) * j + (47 ) * m + (-839 ))
+ (H5 : 0 <= (-1 ) * i + 1 * j + (-1 ))
+ (H6 : 0 <= (-1 ) * j + 1 * m + (0 ))
+ (H7 : 0 <= (1 ) * j + (5 ) * m + (-27 ))
+ (H8 : 0 <= (2 ) * j + (-1 ) * m + (2 ))
+ (H9 : 0 <= (7 ) * j + (10 ) * m + (-74 ))
+ (H10 : 0 <= (18 ) * j + (-139 ) * m + (1188 ))
+ (H11 : 0 <= 1 * i + (0 ))
+ (H13 : 0 <= (121 ) * i + (810 ) * j + (-7465 ) * m + (64350 )),
+ (( 1 ) = (-2 ) * i + it).
+Proof.
+ intros.
+ omicron R.
+Qed.
diff --git a/test-suite/micromega/square.v b/test-suite/micromega/square.v
new file mode 100644
index 00000000..30c72e8c
--- /dev/null
+++ b/test-suite/micromega/square.v
@@ -0,0 +1,61 @@
+(************************************************************************)
+(* *)
+(* Micromega: A reflexive tactic using the Positivstellensatz *)
+(* *)
+(* Frédéric Besson (Irisa/Inria) 2006-2008 *)
+(* *)
+(************************************************************************)
+
+Require Import ZArith Zwf Micromegatac QArith.
+Open Scope Z_scope.
+
+Lemma Zabs_square : forall x, (Zabs x)^2 = x^2.
+Proof.
+ intros ; case (Zabs_dec x) ; intros ; micromega Z.
+Qed.
+Hint Resolve Zabs_pos Zabs_square.
+
+Lemma integer_statement : ~exists n, exists p, n^2 = 2*p^2 /\ n <> 0.
+Proof.
+intros [n [p [Heq Hnz]]]; pose (n' := Zabs n); pose (p':=Zabs p).
+assert (facts : 0 <= Zabs n /\ 0 <= Zabs p /\ Zabs n^2=n^2
+ /\ Zabs p^2 = p^2) by auto.
+assert (H : (0 < n' /\ 0 <= p' /\ n' ^2 = 2* p' ^2)) by
+ (destruct facts as [Hf1 [Hf2 [Hf3 Hf4]]]; unfold n', p' ; micromega Z).
+generalize p' H; elim n' using (well_founded_ind (Zwf_well_founded 0)); clear.
+intros n IHn p [Hn [Hp Heq]].
+assert (Hzwf : Zwf 0 (2*p-n) n) by (unfold Zwf; micromega Z).
+assert (Hdecr : 0 < 2*p-n /\ 0 <= n-p /\ (2*p-n)^2=2*(n-p)^2) by micromega Z.
+apply (IHn (2*p-n) Hzwf (n-p) Hdecr).
+Qed.
+
+Open Scope Q_scope.
+
+Lemma QnumZpower : forall x : Q, Qnum (x ^ 2)%Q = ((Qnum x) ^ 2) %Z.
+Proof.
+ intros.
+ destruct x.
+ cbv beta iota zeta delta - [Zmult].
+ ring.
+Qed.
+
+
+Lemma QdenZpower : forall x : Q, ' Qden (x ^ 2)%Q = ('(Qden x) ^ 2) %Z.
+Proof.
+ intros.
+ destruct x.
+ cbv beta iota zeta delta - [Pmult].
+ rewrite Pmult_1_r.
+ reflexivity.
+Qed.
+
+Theorem sqrt2_not_rational : ~exists x:Q, x^2==2#1.
+Proof.
+ unfold Qeq; intros [x]; simpl (Qden (2#1)); rewrite Zmult_1_r.
+ intros HQeq.
+ assert (Heq : (Qnum x ^ 2 = 2 * ' Qden x ^ 2%Q)%Z) by
+ (rewrite QnumZpower in HQeq ; rewrite QdenZpower in HQeq ; auto).
+ assert (Hnx : (Qnum x <> 0)%Z)
+ by (intros Hx; simpl in HQeq; rewrite Hx in HQeq; discriminate HQeq).
+ apply integer_statement; exists (Qnum x); exists (' Qden x); auto.
+Qed.
diff --git a/test-suite/micromega/zomicron.v b/test-suite/micromega/zomicron.v
new file mode 100644
index 00000000..b13654d6
--- /dev/null
+++ b/test-suite/micromega/zomicron.v
@@ -0,0 +1,27 @@
+Require Import ZArith.
+Require Import Micromegatac.
+Open Scope Z_scope.
+
+Lemma two_x_eq_1 : forall x, 2 * x = 1 -> False.
+Proof.
+ intros.
+ omicron Z.
+Qed.
+
+Lemma two_x_y_eq_1 : forall x y, 2 * x + 2 * y = 1 -> False.
+Proof.
+ intros.
+ omicron Z.
+Qed.
+
+Lemma two_x_y_z_eq_1 : forall x y z, 2 * x + 2 * y + 2 * z= 1 -> False.
+Proof.
+ intros.
+ omicron Z.
+Qed.
+
+Lemma omega_nightmare : forall x y, 27 <= 11 * x + 13 * y <= 45 -> 7 * x - 9 * y = 4 -> -10 <= 7 * x - 9 * y <= 4 -> False.
+Proof.
+ intros ; intuition auto.
+ omicron Z.
+Qed.
diff --git a/test-suite/modules/pseudo_circular_with.v b/test-suite/modules/pseudo_circular_with.v
new file mode 100644
index 00000000..9e46d17e
--- /dev/null
+++ b/test-suite/modules/pseudo_circular_with.v
@@ -0,0 +1,6 @@
+Module Type S. End S.
+Module Type T. Declare Module M:S. End T.
+Module N:S. End N.
+
+Module NN:T. Module M:=N. End NN.
+Module Type U := T with Module M:=NN. \ No newline at end of file
diff --git a/test-suite/modules/resolver.v b/test-suite/modules/resolver.v
new file mode 100644
index 00000000..dcfcc98d
--- /dev/null
+++ b/test-suite/modules/resolver.v
@@ -0,0 +1,37 @@
+Module Type TA.
+Parameter t : Set.
+End TA.
+
+Module Type TB.
+Declare Module A: TA.
+End TB.
+
+Module Type TC.
+Declare Module B : TB.
+End TC.
+
+Module Type TD.
+
+Declare Module B: TB .
+Declare Module C: TC
+ with Module B := B .
+End TD.
+
+Module Type TE.
+Declare Module D : TD.
+End TE.
+
+Module Type TF.
+Declare Module E: TE.
+End TF.
+
+Module G (D: TD).
+Module B' := D.C.B.
+End G.
+
+Module H (F: TF).
+Module I := G(F.E.D).
+End H.
+
+Declare Module F: TF.
+Module K := H(F).
diff --git a/test-suite/modules/subtyping.v b/test-suite/modules/subtyping.v
new file mode 100644
index 00000000..2df8e84e
--- /dev/null
+++ b/test-suite/modules/subtyping.v
@@ -0,0 +1,46 @@
+(* Non regression for bug #1302 *)
+
+(* With universe polymorphism for inductive types, subtyping of
+ inductive types needs a special treatment: the standard conversion
+ algorithm does not work as it only knows to deal with constraints of
+ the form alpha = beta or max(alphas, alphas+1) <= beta, while
+ subtyping of inductive types in Type generates constraints of the form
+ max(alphas, alphas+1) <= max(betas, betas+1).
+
+ These constraints are anyway valid by monotonicity of subtyping but we
+ have to detect it early enough to avoid breaking the standard
+ algorithm for constraints on algebraic universes. *)
+
+Module Type T.
+
+ Parameter A : Type (* Top.1 *) .
+
+ Inductive L : Type (* max(Top.1,1) *) :=
+ | L0
+ | L1 : (A -> Prop) -> L.
+
+End T.
+
+Axiom Tp : Type (* Top.5 *) .
+
+Module TT : T.
+
+ Definition A : Type (* Top.6 *) := Tp. (* generates Top.5 <= Top.6 *)
+
+ Inductive L : Type (* max(Top.6,1) *) :=
+ | L0
+ | L1 : (A -> Prop) -> L.
+
+End TT. (* Generates Top.6 <= Top.1 (+ auxiliary constraints for L_rect) *)
+
+(* Note: Top.6 <= Top.1 is generated by subtyping on A;
+ subtyping of L follows and has not to be checked *)
+
+
+
+(* The same bug as #1302 but for Definition *)
+(* Check that inferred algebraic universes in interfaces are considered *)
+
+Module Type U. Definition A := Type -> Type. End U.
+Module M:U. Definition A := Type -> Type. End M.
+
diff --git a/test-suite/output/Cases.out b/test-suite/output/Cases.out
index a3033e94..9d0d0658 100644
--- a/test-suite/output/Cases.out
+++ b/test-suite/output/Cases.out
@@ -6,4 +6,25 @@ fix F (t : t) : P t :=
end
: forall P : t -> Type,
(let x := t in forall x0 : x, P x0 -> P (k x0)) -> forall t : t, P t
+proj =
+fun (x y : nat) (P : nat -> Type) (def : P x) (prf : P y) =>
+match eq_nat_dec x y with
+| left eqprf =>
+ match eqprf in (_ = z) return (P z) with
+ | refl_equal => def
+ end
+| right _ => prf
+end
+ : forall (x y : nat) (P : nat -> Type), P x -> P y -> P y
+Argument scopes are [nat_scope nat_scope _ _ _]
+foo =
+fix foo (A : Type) (l : list A) {struct l} : option A :=
+ match l with
+ | nil => None (A:=A)
+ | x0 :: nil => Some x0
+ | x0 :: (_ :: _) as l0 => foo A l0
+ end
+ : forall A : Type, list A -> option A
+
+Argument scopes are [type_scope list_scope]
diff --git a/test-suite/output/Cases.v b/test-suite/output/Cases.v
index 452d3603..61f89d40 100644
--- a/test-suite/output/Cases.v
+++ b/test-suite/output/Cases.v
@@ -4,3 +4,32 @@ Inductive t : Set :=
k : let x := t in x -> x.
Print t_rect.
+
+(* Do not contract nested patterns with dependent return type *)
+(* see bug #1699 *)
+
+Require Import Arith.
+
+Definition proj (x y:nat) (P:nat -> Type) (def:P x) (prf:P y) : P y :=
+ match eq_nat_dec x y return P y with
+ | left eqprf =>
+ match eqprf in (_ = z) return (P z) with
+ | refl_equal => def
+ end
+ | _ => prf
+ end.
+
+Print proj.
+
+(* Use notations even below aliases *)
+
+Require Import List.
+
+Fixpoint foo (A:Type) (l:list A) : option A :=
+ match l with
+ | nil => None
+ | x0 :: nil => Some x0
+ | x0 :: (x1 :: xs) as l0 => foo A l0
+ end.
+
+Print foo.
diff --git a/test-suite/output/Fixpoint.out b/test-suite/output/Fixpoint.out
index 62c9d395..f4270d3d 100644
--- a/test-suite/output/Fixpoint.out
+++ b/test-suite/output/Fixpoint.out
@@ -9,3 +9,17 @@ let fix f (m : nat) : nat := match m with
| S m' => f m'
end in f 0
: nat
+fix even_pos_odd_pos 2
+ with (odd_pos_even_pos (n:_) (H:odd n) {struct H} : n >= 1).
+ intros.
+ destruct H.
+ omega.
+
+ apply odd_pos_even_pos in H.
+ omega.
+
+ intros.
+ destruct H.
+ apply even_pos_odd_pos in H.
+ omega.
+
diff --git a/test-suite/output/Fixpoint.v b/test-suite/output/Fixpoint.v
index fc27e8d2..2b13c204 100644
--- a/test-suite/output/Fixpoint.v
+++ b/test-suite/output/Fixpoint.v
@@ -16,3 +16,26 @@ Check
end
in f 0.
+Require Import ZArith_base Omega.
+Open Scope Z_scope.
+
+Inductive even: Z -> Prop :=
+| even_base: even 0
+| even_succ: forall n, odd (n - 1) -> even n
+with odd: Z -> Prop :=
+| odd_succ: forall n, even (n - 1) -> odd n.
+
+Lemma even_pos_odd_pos: forall n, even n -> n >= 0.
+Proof.
+fix even_pos_odd_pos 2 with (odd_pos_even_pos n (H:odd n) {struct H} : n >= 1).
+ intros.
+ destruct H.
+ omega.
+ apply odd_pos_even_pos in H.
+ omega.
+ intros.
+ destruct H.
+ apply even_pos_odd_pos in H.
+ omega.
+Show Script.
+Qed.
diff --git a/test-suite/output/Implicit.out b/test-suite/output/Implicit.out
index 38c5b827..ecfe8505 100644
--- a/test-suite/output/Implicit.out
+++ b/test-suite/output/Implicit.out
@@ -5,6 +5,9 @@ ex_intro (P:=fun _ : nat => True) (x:=0) I
d2 = fun x : nat => d1 (y:=x)
: forall x x0 : nat, x0 = x -> x0 = x
-
Arguments x, x0 are implicit
Argument scopes are [nat_scope nat_scope _]
+map id (1 :: nil)
+ : list nat
+map id' (1 :: nil)
+ : list nat
diff --git a/test-suite/output/Implicit.v b/test-suite/output/Implicit.v
index 0ff7e87f..4c6f2b5d 100644
--- a/test-suite/output/Implicit.v
+++ b/test-suite/output/Implicit.v
@@ -17,3 +17,22 @@ Definition d1 y x (h : x = y :>nat) := h.
Definition d2 x := d1 (y:=x).
Print d2.
+
+(* Check maximal insertion of implicit *)
+
+Require Import List.
+
+Open Scope list_scope.
+
+Set Implicit Arguments.
+Set Maximal Implicit Insertion.
+
+Definition id (A:Type) (x:A) := x.
+
+Check map id (1::nil).
+
+Definition id' (A:Type) (x:A) := x.
+
+Implicit Arguments id' [[A]].
+
+Check map id' (1::nil).
diff --git a/test-suite/output/InitSyntax.out b/test-suite/output/InitSyntax.out
index c7f3ed7d..9299e010 100644
--- a/test-suite/output/InitSyntax.out
+++ b/test-suite/output/InitSyntax.out
@@ -1,5 +1,6 @@
-Inductive sig2 (A : Type) (P : A -> Prop) (Q : A -> Prop) : Type :=
+Inductive sig2 (A : Type) (P Q : A -> Prop) : Type :=
exist2 : forall x : A, P x -> Q x -> sig2 P Q
+
For sig2: Argument A is implicit
For exist2: Argument A is implicit
For sig2: Argument scopes are [type_scope type_scope type_scope]
diff --git a/test-suite/output/Nametab.out b/test-suite/output/Nametab.out
index d0f15f0e..b1883ec0 100644
--- a/test-suite/output/Nametab.out
+++ b/test-suite/output/Nametab.out
@@ -1,12 +1,12 @@
-Constant Top.Q.N.K.id
- (shorter name to refer to it in current context is Q.N.K.id)
-Constant Top.Q.N.K.id
- (shorter name to refer to it in current context is Q.N.K.id)
-Constant Top.Q.N.K.id
- (shorter name to refer to it in current context is Q.N.K.id)
-Constant Top.Q.N.K.id
-Constant Top.Q.N.K.id
- (shorter name to refer to it in current context is Q.N.K.id)
+Constant Top.Q.N.K.foo
+ (shorter name to refer to it in current context is Q.N.K.foo)
+Constant Top.Q.N.K.foo
+ (shorter name to refer to it in current context is Q.N.K.foo)
+Constant Top.Q.N.K.foo
+ (shorter name to refer to it in current context is Q.N.K.foo)
+Constant Top.Q.N.K.foo
+Constant Top.Q.N.K.foo
+ (shorter name to refer to it in current context is Q.N.K.foo)
No module is referred to by basename K
No module is referred to by name N.K
Module Top.Q.N.K
@@ -16,15 +16,15 @@ Module Top.Q.N
Module Top.Q.N
Module Top.Q
Module Top.Q
-Constant Top.Q.N.K.id
- (shorter name to refer to it in current context is K.id)
-Constant Top.Q.N.K.id
-Constant Top.Q.N.K.id
- (shorter name to refer to it in current context is K.id)
-Constant Top.Q.N.K.id
- (shorter name to refer to it in current context is K.id)
-Constant Top.Q.N.K.id
- (shorter name to refer to it in current context is K.id)
+Constant Top.Q.N.K.foo
+ (shorter name to refer to it in current context is K.foo)
+Constant Top.Q.N.K.foo
+Constant Top.Q.N.K.foo
+ (shorter name to refer to it in current context is K.foo)
+Constant Top.Q.N.K.foo
+ (shorter name to refer to it in current context is K.foo)
+Constant Top.Q.N.K.foo
+ (shorter name to refer to it in current context is K.foo)
Module Top.Q.N.K
No module is referred to by name N.K
Module Top.Q.N.K
diff --git a/test-suite/output/Nametab.v b/test-suite/output/Nametab.v
index a1a7579b..357ba982 100644
--- a/test-suite/output/Nametab.v
+++ b/test-suite/output/Nametab.v
@@ -1,16 +1,16 @@
Module Q.
Module N.
Module K.
- Definition id := Set.
+ Definition foo := Set.
End K.
End N.
End Q.
-(* Bad *) Locate id.
-(* Bad *) Locate K.id.
-(* Bad *) Locate N.K.id.
-(* OK *) Locate Q.N.K.id.
-(* OK *) Locate Top.Q.N.K.id.
+(* Bad *) Locate foo.
+(* Bad *) Locate K.foo.
+(* Bad *) Locate N.K.foo.
+(* OK *) Locate Q.N.K.foo.
+(* OK *) Locate Top.Q.N.K.foo.
(* Bad *) Locate Module K.
(* Bad *) Locate Module N.K.
@@ -28,11 +28,11 @@ End Q.
Import Q.N.
-(* Bad *) Locate id.
-(* OK *) Locate K.id.
-(* Bad *) Locate N.K.id.
-(* OK *) Locate Q.N.K.id.
-(* OK *) Locate Top.Q.N.K.id.
+(* Bad *) Locate foo.
+(* OK *) Locate K.foo.
+(* Bad *) Locate N.K.foo.
+(* OK *) Locate Q.N.K.foo.
+(* OK *) Locate Top.Q.N.K.foo.
(* OK *) Locate Module K.
(* Bad *) Locate Module N.K.
diff --git a/test-suite/output/Notations.out b/test-suite/output/Notations.out
index be4cd4fa..2066a7ef 100644
--- a/test-suite/output/Notations.out
+++ b/test-suite/output/Notations.out
@@ -46,3 +46,7 @@ fun x : nat => ifn x is succ n then n else 0
: bool
-4
: Z
+Nil
+ : forall A : Type, list A
+NIL:list nat
+ : list nat
diff --git a/test-suite/output/Notations.v b/test-suite/output/Notations.v
index 3cc0a189..6e637aca 100644
--- a/test-suite/output/Notations.v
+++ b/test-suite/output/Notations.v
@@ -119,3 +119,13 @@ Require Import ZArith.
Open Scope Z_scope.
Notation "- 4" := (-2 + -2).
Check -4.
+
+(**********************************************************************)
+(* Check notations for references with activated or deactivated *)
+(* implicit arguments *)
+
+Notation Nil := @nil.
+Check Nil.
+
+Notation NIL := nil.
+Check NIL : list nat.
diff --git a/test-suite/output/Tactics.out b/test-suite/output/Tactics.out
index 8e8b8059..287e8488 100644
--- a/test-suite/output/Tactics.out
+++ b/test-suite/output/Tactics.out
@@ -1,4 +1,6 @@
intro H; split; [ a H | e H ].
+
intros; match goal with
| |- context [if ?X then _ else _] => case X
end; trivial.
+
diff --git a/test-suite/output/TranspModtype.out b/test-suite/output/TranspModtype.out
index 41e8648b..f94ed642 100644
--- a/test-suite/output/TranspModtype.out
+++ b/test-suite/output/TranspModtype.out
@@ -1,10 +1,7 @@
TrM.A = M.A
: Set
-
OpM.A = M.A
: Set
-
TrM.B = M.B
: Set
-
*** [ OpM.B : Set ]
diff --git a/test-suite/output/ZSyntax.out b/test-suite/output/ZSyntax.out
index cbfb9f20..f23198b0 100644
--- a/test-suite/output/ZSyntax.out
+++ b/test-suite/output/ZSyntax.out
@@ -2,19 +2,19 @@
: Z
fun f : nat -> Z => (f 0%nat + 0)%Z
: (nat -> Z) -> Z
-fun x : positive => Zpos (xO x)
+fun x : positive => Zpos x~0
: positive -> Z
fun x : positive => (Zpos x + 1)%Z
: positive -> Z
fun x : positive => Zpos x
: positive -> Z
-fun x : positive => Zneg (xO x)
+fun x : positive => Zneg x~0
: positive -> Z
-fun x : positive => (Zpos (xO x) + 0)%Z
+fun x : positive => (Zpos x~0 + 0)%Z
: positive -> Z
-fun x : positive => (- Zpos (xO x))%Z
+fun x : positive => (- Zpos x~0)%Z
: positive -> Z
-fun x : positive => (- Zpos (xO x) + 0)%Z
+fun x : positive => (- Zpos x~0 + 0)%Z
: positive -> Z
(Z_of_nat 0 + 1)%Z
: Z
diff --git a/test-suite/output/reduction.out b/test-suite/output/reduction.out
new file mode 100644
index 00000000..ff327aa5
--- /dev/null
+++ b/test-suite/output/reduction.out
@@ -0,0 +1,4 @@
+ = a
+ : nat
+ = n + 0
+ : nat
diff --git a/test-suite/output/reduction.v b/test-suite/output/reduction.v
new file mode 100644
index 00000000..4a460a83
--- /dev/null
+++ b/test-suite/output/reduction.v
@@ -0,0 +1,13 @@
+(* Test the behaviour of hnf and simpl introduced in revision *)
+
+Variable n:nat.
+Definition a:=0.
+
+Eval simpl in (fix plus (n m : nat) {struct n} : nat :=
+ match n with
+ | 0 => m
+ | S p => S (p + m)
+ end) a a.
+
+Eval hnf in match (plus (S n) O) with S n => n | _ => O end.
+
diff --git a/test-suite/success/AdvancedCanonicalStructure.v b/test-suite/success/AdvancedCanonicalStructure.v
new file mode 100644
index 00000000..8e613dca
--- /dev/null
+++ b/test-suite/success/AdvancedCanonicalStructure.v
@@ -0,0 +1,144 @@
+Section group_morphism.
+
+(* An example with default canonical structures *)
+
+Variable A B : Type.
+Variable plusA : A -> A -> A.
+Variable plusB : B -> B -> B.
+Variable zeroA : A.
+Variable zeroB : B.
+Variable eqA : A -> A -> Prop.
+Variable eqB : B -> B -> Prop.
+Variable phi : A -> B.
+
+Record img := {
+ ia : A;
+ ib :> B;
+ prf : phi ia = ib
+}.
+
+Parameter eq_img : forall (i1:img) (i2:img),
+ eqB (ib i1) (ib i2) -> eqA (ia i1) (ia i2).
+
+Lemma phi_img (a:A) : img.
+ intro a.
+ exists a (phi a).
+ refine ( refl_equal _).
+Defined.
+Canonical Structure phi_img.
+
+Lemma zero_img : img.
+ exists zeroA zeroB.
+ admit.
+Defined.
+Canonical Structure zero_img.
+
+Lemma plus_img : img -> img -> img.
+intros i1 i2.
+exists (plusA (ia i1) (ia i2)) (plusB (ib i1) (ib i2)).
+admit.
+Defined.
+Canonical Structure plus_img.
+
+(* Print Canonical Projections. *)
+
+Goal forall a1 a2, eqA (plusA a1 zeroA) a2.
+ intros a1 a2.
+ refine (eq_img _ _ _).
+change (eqB (plusB (phi a1) zeroB) (phi a2)).
+Admitted.
+
+End group_morphism.
+
+Open Scope type_scope.
+
+Section type_reification.
+
+Inductive term :Type :=
+ Fun : term -> term -> term
+ | Prod : term -> term -> term
+ | Bool : term
+ | SET :term
+ | PROP :term
+ | TYPE :term
+ | Var : Type -> term.
+
+Fixpoint interp (t:term) :=
+ match t with
+ Bool => bool
+ | SET => Set
+ | PROP => Prop
+ | TYPE => Type
+ | Fun a b => interp a -> interp b
+ | Prod a b => interp a * interp b
+ | Var x => x
+end.
+
+Record interp_pair :Type :=
+ { repr:>term;
+ abs:>Type;
+ link: abs = interp repr }.
+
+Lemma prod_interp :forall (a b:interp_pair),a * b = interp (Prod a b) .
+proof.
+let a:interp_pair,b:interp_pair.
+reconsider thesis as (a * b = interp a * interp b).
+thus thesis by (link a),(link b).
+end proof.
+Qed.
+
+Lemma fun_interp :forall (a b:interp_pair), (a -> b) = interp (Fun a b).
+proof.
+let a:interp_pair,b:interp_pair.
+reconsider thesis as ((a -> b) = (interp a -> interp b)).
+thus thesis using rewrite (link a);rewrite (link b);reflexivity.
+end proof.
+Qed.
+
+Canonical Structure ProdCan (a b:interp_pair) :=
+ Build_interp_pair (Prod a b) (a * b) (prod_interp a b).
+
+Canonical Structure FunCan (a b:interp_pair) :=
+ Build_interp_pair (Fun a b) (a -> b) (fun_interp a b).
+
+Canonical Structure BoolCan :=
+ Build_interp_pair Bool bool (refl_equal _).
+
+Canonical Structure VarCan (x:Type) :=
+ Build_interp_pair (Var x) x (refl_equal _).
+
+Canonical Structure SetCan :=
+ Build_interp_pair SET Set (refl_equal _).
+
+Canonical Structure PropCan :=
+ Build_interp_pair PROP Prop (refl_equal _).
+
+Canonical Structure TypeCan :=
+ Build_interp_pair TYPE Type (refl_equal _).
+
+(* Print Canonical Projections. *)
+
+Variable A:Type.
+
+Variable Inhabited: term -> Prop.
+
+Variable Inhabited_correct: forall p, Inhabited (repr p) -> abs p.
+
+Lemma L : Prop * A -> bool * (Type -> Set) .
+refine (Inhabited_correct _ _).
+change (Inhabited (Fun (Prod PROP (Var A)) (Prod Bool (Fun TYPE SET)))).
+Admitted.
+
+Check L : abs _ .
+
+End type_reification.
+
+
+
+
+
+
+
+
+
+
diff --git a/test-suite/success/Case18.v b/test-suite/success/Case18.v
index 91c80e88..be9ca8d4 100644
--- a/test-suite/success/Case18.v
+++ b/test-suite/success/Case18.v
@@ -12,3 +12,15 @@ Fixpoint max (n m:nat) {struct m} : nat :=
| S n', S m' => S (max n' m')
| 0, p | p, 0 => p
end.
+
+(* Check bug #1477 *)
+
+Inductive I : Set :=
+ | A : nat -> nat -> I
+ | B : nat -> nat -> I.
+
+Definition foo (x:I) : nat :=
+ match x with
+ | A a b | B b a => S b
+ end.
+
diff --git a/test-suite/success/Cases-bug1834.v b/test-suite/success/Cases-bug1834.v
new file mode 100644
index 00000000..543ca0c9
--- /dev/null
+++ b/test-suite/success/Cases-bug1834.v
@@ -0,0 +1,13 @@
+(* Bug in the computation of generalization *)
+
+(* The following bug, elaborated by Bruno Barras, is solved from r11083 *)
+
+Parameter P : unit -> Prop.
+Definition T := sig P.
+Parameter Q : T -> Prop.
+Definition U := sig Q.
+Parameter a : U.
+Check (match a with exist (exist tt e2) e3 => e3=e3 end).
+
+(* There is still a form submitted by Pierre Corbineau (#1834) which fails *)
+
diff --git a/test-suite/success/Cases.v b/test-suite/success/Cases.v
index 7c2b7c0b..499c0660 100644
--- a/test-suite/success/Cases.v
+++ b/test-suite/success/Cases.v
@@ -10,6 +10,10 @@ Type match 0, eq, 0 return nat with
| O, x, y => 0
| S x, y, z => x
end.
+Type match 0, eq, 0 return _ with
+ | O, x, y => 0
+ | S x, y, z => x
+ end.
(* Non dependent form of annotation *)
Type match 0, eq return nat with
@@ -406,7 +410,6 @@ Type match niln with
| x => 0
end.
-
Type match niln return nat with
| niln => 0
| consn n a l => a
diff --git a/test-suite/success/CasesDep.v b/test-suite/success/CasesDep.v
index 0477377e..49bd77fc 100644
--- a/test-suite/success/CasesDep.v
+++ b/test-suite/success/CasesDep.v
@@ -71,13 +71,9 @@ Inductive Setoid : Type :=
Definition elem (A : Setoid) := let (S, R, e) := A in S.
-(* <Warning> : Grammar is replaced by Notation *)
-
Definition equal (A : Setoid) :=
let (S, R, e) as s return (Relation (elem s)) := A in R.
-(* <Warning> : Grammar is replaced by Notation *)
-
Axiom prf_equiv : forall A : Setoid, Equivalence (elem A) (equal A).
Axiom prf_refl : forall A : Setoid, Reflexive (elem A) (equal A).
@@ -430,3 +426,57 @@ Definition f0 (F : False) (ty : bool) : bProp ty :=
| _, false => F
| _, true => I
end.
+
+(* Simplification of bug/wish #1671 *)
+
+Inductive I : unit -> Type :=
+| C : forall a, I a -> I tt.
+
+(*
+Definition F (l:I tt) : l = l :=
+match l return l = l with
+| C tt (C _ l') => refl_equal (C tt (C _ l'))
+end.
+
+one would expect that the compilation of F (this involves
+some kind of pattern-unification) would produce:
+*)
+
+Definition F (l:I tt) : l = l :=
+match l return l = l with
+| C tt l' => match l' return C _ l' = C _ l' with C _ l'' => refl_equal (C tt (C _ l'')) end
+end.
+
+Inductive J : nat -> Type :=
+| D : forall a, J (S a) -> J a.
+
+(*
+Definition G (l:J O) : l = l :=
+match l return l = l with
+| D O (D 1 l') => refl_equal (D O (D 1 l'))
+| D _ _ => refl_equal _
+end.
+
+one would expect that the compilation of G (this involves inversion)
+would produce:
+*)
+
+Definition G (l:J O) : l = l :=
+match l return l = l with
+| D 0 l'' =>
+ match l'' as _l'' in J n return
+ match n return forall l:J n, Prop with
+ | O => fun _ => l = l
+ | S p => fun l'' => D p l'' = D p l''
+ end _l'' with
+ | D 1 l' => refl_equal (D O (D 1 l'))
+ | _ => refl_equal _
+ end
+| _ => refl_equal _
+end.
+
+Fixpoint app {A} {n m} (v : listn A n) (w : listn A m) : listn A (n + m) :=
+ match v with
+ | niln => w
+ | consn a n' v' => consn _ a _ (app v' w)
+ end.
diff --git a/test-suite/success/Discriminate.v b/test-suite/success/Discriminate.v
index f28c83de..b57c5478 100644
--- a/test-suite/success/Discriminate.v
+++ b/test-suite/success/Discriminate.v
@@ -9,3 +9,26 @@ Qed.
Lemma l2 : forall H : 0 = 1, H = H.
discriminate H.
Qed.
+
+(* Check the variants of discriminate *)
+
+Goal O = S O -> True.
+discriminate 1.
+Undo.
+intros.
+discriminate H.
+Undo.
+Ltac g x := discriminate x.
+g H.
+Abort.
+
+Goal (forall x y : nat, x = y -> x = S y) -> True.
+intros.
+try discriminate (H O) || exact I.
+Qed.
+
+Goal (forall x y : nat, x = y -> x = S y) -> True.
+intros.
+ediscriminate (H O).
+instantiate (1:=O).
+Abort.
diff --git a/test-suite/success/Fixpoint.v b/test-suite/success/Fixpoint.v
index 680046da..cf821073 100644
--- a/test-suite/success/Fixpoint.v
+++ b/test-suite/success/Fixpoint.v
@@ -29,3 +29,22 @@ CoFixpoint g (n:nat) (m:=pred n) (l:Stream m) (p:=S n) : Stream p :=
Eval compute in (fun l => match g 2 (Consn 0 6 l) with Consn _ a _ => a end).
+(* Check inference of simple types in presence of non ambiguous
+ dependencies (needs revision 10125) *)
+
+Section folding.
+
+Inductive vector (A:Type) : nat -> Type :=
+ | Vnil : vector A 0
+ | Vcons : forall (a:A) (n:nat), vector A n -> vector A (S n).
+
+Variables (B C : Set) (g : B -> C -> C) (c : C).
+
+Fixpoint foldrn n bs :=
+ match bs with
+ | Vnil => c
+ | Vcons b _ tl => g b (foldrn _ tl)
+ end.
+
+End folding.
+
diff --git a/test-suite/success/ImplicitArguments.v b/test-suite/success/ImplicitArguments.v
new file mode 100644
index 00000000..e7795733
--- /dev/null
+++ b/test-suite/success/ImplicitArguments.v
@@ -0,0 +1,17 @@
+Inductive vector {A : Type} : nat -> Type :=
+| vnil : vector 0
+| vcons : A -> forall {n'}, vector n' -> vector (S n').
+
+Require Import Coq.Program.Program.
+
+Program Definition head {A : Type} {n : nat} (v : vector A (S n)) : vector A n :=
+ match v with
+ | vnil => !
+ | vcons a n' v' => v'
+ end.
+
+Fixpoint app {A : Type} {n m : nat} (v : vector A n) (w : vector A m) : vector A (n + m) :=
+ match v in vector _ n return vector A (n + m) with
+ | vnil => w
+ | vcons a n' v' => vcons a (app v' w)
+ end.
diff --git a/test-suite/success/Injection.v b/test-suite/success/Injection.v
index 606e884a..867d7374 100644
--- a/test-suite/success/Injection.v
+++ b/test-suite/success/Injection.v
@@ -43,6 +43,29 @@ intros; injection H as Hyt Hxz.
exact Hxz.
Qed.
+(* Check the variants of injection *)
+
+Goal forall x y, S x = S y -> True.
+injection 1 as H'.
+Undo.
+intros.
+injection H as H'.
+Undo.
+Ltac f x := injection x.
+f H.
+Abort.
+
+Goal (forall x y : nat, x = y -> S x = S y) -> True.
+intros.
+try injection (H O) || exact I.
+Qed.
+
+Goal (forall x y : nat, x = y -> S x = S y) -> True.
+intros.
+einjection (H O).
+instantiate (1:=O).
+Abort.
+
(* Injection does not projects at positions in Prop... allow it?
Inductive t (A:Prop) : Set := c : A -> t A.
@@ -53,7 +76,7 @@ Abort.
*)
-(* Accept does not project on discriminable positions... allow it?
+(* Injection does not project on discriminable positions... allow it?
Goal 1=2 -> 1=0.
intro H.
@@ -61,4 +84,4 @@ injection H.
intro; assumption.
Qed.
- *)
+*)
diff --git a/test-suite/success/LetPat.v b/test-suite/success/LetPat.v
new file mode 100644
index 00000000..545b8aeb
--- /dev/null
+++ b/test-suite/success/LetPat.v
@@ -0,0 +1,55 @@
+(* Simple let-patterns *)
+Variable A B : Type.
+
+Definition l1 (t : A * B * B) : A := let '(x, y, z) := t in x.
+Print l1.
+Definition l2 (t : (A * B) * B) : A := let '((x, y), z) := t in x.
+Definition l3 (t : A * (B * B)) : A := let '(x, (y, z)) := t in x.
+Print l3.
+
+Record someT (A : Type) := mkT { a : nat; b: A }.
+
+Definition l4 A (t : someT A) : nat := let 'mkT x y := t in x.
+Print l4.
+Print sigT.
+
+Definition l5 A (B : A -> Type) (t : sigT B) : B (projT1 t) :=
+ let 'existT x y := t return B (projT1 t) in y.
+
+Definition l6 A (B : A -> Type) (t : sigT B) : B (projT1 t) :=
+ let 'existT x y as t' := t return B (projT1 t') in y.
+
+Definition l7 A (B : A -> Type) (t : sigT B) : B (projT1 t) :=
+ let 'existT x y as t' in sigT _ := t return B (projT1 t') in y.
+
+Definition l8 A (B : A -> Type) (t : sigT B) : B (projT1 t) :=
+ match t with
+ existT x y => y
+ end.
+
+(** An example from algebra, using let' and inference of return clauses
+ to deconstruct contexts. *)
+
+Record a_category (A : Type) (hom : A -> A -> Type) := { }.
+
+Definition category := { A : Type & { hom : A -> A -> Type & a_category A hom } }.
+
+Record a_functor (A : Type) (hom : A -> A -> Type) (C : a_category A hom) := { }.
+
+Notation " x :& y " := (@existT _ _ x y) (right associativity, at level 55) : core_scope.
+
+Definition functor (c d : category) :=
+ let ' A :& homA :& CA := c in
+ let ' B :& homB :& CB := d in
+ A -> B.
+
+Definition identity_functor (c : category) : functor c c :=
+ let 'A :& homA :& CA := c in
+ fun x => x.
+
+Definition functor_composition (a b c : category) : functor a b -> functor b c -> functor a c :=
+ let 'A :& homA :& CA := a in
+ let 'B :& homB :& CB := b in
+ let 'C :& homB :& CB := c in
+ fun f g =>
+ fun x => g (f x).
diff --git a/test-suite/success/Notations.v b/test-suite/success/Notations.v
index a9e2c59a..facd5509 100644
--- a/test-suite/success/Notations.v
+++ b/test-suite/success/Notations.v
@@ -1,5 +1,5 @@
(* Check that "where" clause behaves as if given independently of the *)
-(* definition (variant of bug #113? submitted by Assia Mahboubi) *)
+(* definition (variant of bug #1132 submitted by Assia Mahboubi) *)
Fixpoint plus1 (n m:nat) {struct n} : nat :=
match n with
@@ -7,3 +7,17 @@ Fixpoint plus1 (n m:nat) {struct n} : nat :=
| S p => S (p+m)
end
where "n + m" := (plus1 n m) : nat_scope.
+
+(* Check behaviour wrt yet empty levels (see Stephane's bug #1850) *)
+
+Parameter P : Type -> Type -> Type -> Type.
+Notation "e |= t --> v" := (P e t v) (at level 100, t at level 54).
+Check (nat |= nat --> nat).
+
+(* Check that first non empty definition at an empty level can be of any
+ associativity *)
+
+Definition marker := O.
+Notation "x +1" := (S x) (at level 8, left associativity).
+Reset marker.
+Notation "x +1" := (S x) (at level 8, right associativity).
diff --git a/test-suite/success/Omega.v b/test-suite/success/Omega.v
index 2d29a835..ecbf04e4 100644
--- a/test-suite/success/Omega.v
+++ b/test-suite/success/Omega.v
@@ -10,14 +10,14 @@ intros x y.
omega.
Qed.
-(* Proposed by Pierre Crégut *)
+(* Proposed by Pierre Crégut *)
Lemma lem2 : forall x : Z, (x < 4)%Z -> (x > 2)%Z -> x = 3%Z.
intro.
omega.
Qed.
-(* Proposed by Jean-Christophe Filliâtre *)
+(* Proposed by Jean-Christophe Filliâtre *)
Lemma lem3 : forall x y : Z, x = y -> (x + x)%Z = (y + y)%Z.
Proof.
@@ -25,7 +25,7 @@ intros.
omega.
Qed.
-(* Proposed by Jean-Christophe Filliâtre: confusion between an Omega *)
+(* Proposed by Jean-Christophe Filliâtre: confusion between an Omega *)
(* internal variable and a section variable (June 2001) *)
Section A.
@@ -87,10 +87,8 @@ Qed.
(* Check that the interpretation of mult on nat enforces its positivity *)
(* Submitted by Hubert Thierry (bug #743) *)
-(* Postponed... problem with goals of the form "(n*m=0)%nat -> (n*m=0)%Z"
-Require Omega.
-Lemma lem10 : (n, m : nat) (le n (plus n (mult n m))).
+(* Postponed... problem with goals of the form "(n*m=0)%nat -> (n*m=0)%Z" *)
+Lemma lem10 : forall n m:nat, le n (plus n (mult n m)).
Proof.
-Intros; Omega.
+intros; omega with *.
Qed.
-*)
diff --git a/test-suite/success/OmegaPre.v b/test-suite/success/OmegaPre.v
new file mode 100644
index 00000000..bb800b7a
--- /dev/null
+++ b/test-suite/success/OmegaPre.v
@@ -0,0 +1,127 @@
+Require Import ZArith Nnat Omega.
+Open Scope Z_scope.
+
+(** Test of the zify preprocessor for (R)Omega *)
+
+(* More details in file PreOmega.v
+
+ (r)omega with Z : starts with zify_op
+ (r)omega with nat : starts with zify_nat
+ (r)omega with positive : starts with zify_positive
+ (r)omega with N : starts with uses zify_N
+ (r)omega with * : starts zify (a saturation of the others)
+*)
+
+(* zify_op *)
+
+Goal forall a:Z, Zmax a a = a.
+intros.
+omega with *.
+Qed.
+
+Goal forall a b:Z, Zmax a b = Zmax b a.
+intros.
+omega with *.
+Qed.
+
+Goal forall a b c:Z, Zmax a (Zmax b c) = Zmax (Zmax a b) c.
+intros.
+omega with *.
+Qed.
+
+Goal forall a b:Z, Zmax a b + Zmin a b = a + b.
+intros.
+omega with *.
+Qed.
+
+Goal forall a:Z, (Zabs a)*(Zsgn a) = a.
+intros.
+zify.
+intuition; subst; omega. (* pure multiplication: omega alone can't do it *)
+Qed.
+
+Goal forall a:Z, Zabs a = a -> a >= 0.
+intros.
+omega with *.
+Qed.
+
+Goal forall a:Z, Zsgn a = a -> a = 1 \/ a = 0 \/ a = -1.
+intros.
+omega with *.
+Qed.
+
+(* zify_nat *)
+
+Goal forall m: nat, (m<2)%nat -> (0<= m+m <=2)%nat.
+intros.
+omega with *.
+Qed.
+
+Goal forall m:nat, (m<1)%nat -> (m=0)%nat.
+intros.
+omega with *.
+Qed.
+
+Goal forall m: nat, (m<=100)%nat -> (0<= m+m <=200)%nat.
+intros.
+omega with *.
+Qed.
+(* 2000 instead of 200: works, but quite slow *)
+
+Goal forall m: nat, (m*m>=0)%nat.
+intros.
+omega with *.
+Qed.
+
+(* zify_positive *)
+
+Goal forall m: positive, (m<2)%positive -> (2 <= m+m /\ m+m <= 2)%positive.
+intros.
+omega with *.
+Qed.
+
+Goal forall m:positive, (m<2)%positive -> (m=1)%positive.
+intros.
+omega with *.
+Qed.
+
+Goal forall m: positive, (m<=1000)%positive -> (2<=m+m/\m+m <=2000)%positive.
+intros.
+omega with *.
+Qed.
+
+Goal forall m: positive, (m*m>=1)%positive.
+intros.
+omega with *.
+Qed.
+
+(* zify_N *)
+
+Goal forall m:N, (m<2)%N -> (0 <= m+m /\ m+m <= 2)%N.
+intros.
+omega with *.
+Qed.
+
+Goal forall m:N, (m<1)%N -> (m=0)%N.
+intros.
+omega with *.
+Qed.
+
+Goal forall m:N, (m<=1000)%N -> (0<=m+m/\m+m <=2000)%N.
+intros.
+omega with *.
+Qed.
+
+Goal forall m:N, (m*m>=0)%N.
+intros.
+omega with *.
+Qed.
+
+(* mix of datatypes *)
+
+Goal forall p, Z_of_N (N_of_nat (nat_of_N (Npos p))) = Zpos p.
+intros.
+omega with *.
+Qed.
+
+
diff --git a/test-suite/success/ROmega.v b/test-suite/success/ROmega.v
index ff1f57df..0c37c59a 100644
--- a/test-suite/success/ROmega.v
+++ b/test-suite/success/ROmega.v
@@ -68,31 +68,29 @@ Variable n : nat.
Variable ap_n : n <> 0.
Let delta := f n ap_n.
Lemma lem7 : n = n.
- (*romega. ---> ROMEGA CANT DEAL WITH NAT*)
-Admitted.
+ romega with nat.
+Qed.
End C.
(* Problem of dependencies *)
Require Import Omega.
Lemma lem8 : forall H : 0 = 0 -> 0 = 0, H = H -> 0 = 0.
intros.
-(* romega. ---> ROMEGA CANT DEAL WITH NAT*)
-Admitted.
+romega with nat.
+Qed.
(* Bug that what caused by the use of intro_using in Omega *)
Require Import Omega.
Lemma lem9 :
forall p q : nat, ~ (p <= q /\ p < q \/ q <= p /\ p < q) -> p < p \/ p <= p.
intros.
-(* romega. ---> ROMEGA CANT DEAL WITH NAT*)
-Admitted.
+romega with nat.
+Qed.
(* Check that the interpretation of mult on nat enforces its positivity *)
(* Submitted by Hubert Thierry (bug #743) *)
-(* Postponed... problem with goals of the form "(n*m=0)%nat -> (n*m=0)%Z"
-Require Omega.
-Lemma lem10 : (n, m : nat) (le n (plus n (mult n m))).
+(* Postponed... problem with goals of the form "(n*m=0)%nat -> (n*m=0)%Z" *)
+Lemma lem10 : forall n m : nat, le n (plus n (mult n m)).
Proof.
-Intros; Omega.
+intros; romega with nat.
Qed.
-*)
diff --git a/test-suite/success/ROmegaPre.v b/test-suite/success/ROmegaPre.v
new file mode 100644
index 00000000..550edca5
--- /dev/null
+++ b/test-suite/success/ROmegaPre.v
@@ -0,0 +1,127 @@
+Require Import ZArith Nnat ROmega.
+Open Scope Z_scope.
+
+(** Test of the zify preprocessor for (R)Omega *)
+
+(* More details in file PreOmega.v
+
+ (r)omega with Z : starts with zify_op
+ (r)omega with nat : starts with zify_nat
+ (r)omega with positive : starts with zify_positive
+ (r)omega with N : starts with uses zify_N
+ (r)omega with * : starts zify (a saturation of the others)
+*)
+
+(* zify_op *)
+
+Goal forall a:Z, Zmax a a = a.
+intros.
+romega with *.
+Qed.
+
+Goal forall a b:Z, Zmax a b = Zmax b a.
+intros.
+romega with *.
+Qed.
+
+Goal forall a b c:Z, Zmax a (Zmax b c) = Zmax (Zmax a b) c.
+intros.
+romega with *.
+Qed.
+
+Goal forall a b:Z, Zmax a b + Zmin a b = a + b.
+intros.
+romega with *.
+Qed.
+
+Goal forall a:Z, (Zabs a)*(Zsgn a) = a.
+intros.
+zify.
+intuition; subst; romega. (* pure multiplication: omega alone can't do it *)
+Qed.
+
+Goal forall a:Z, Zabs a = a -> a >= 0.
+intros.
+romega with *.
+Qed.
+
+Goal forall a:Z, Zsgn a = a -> a = 1 \/ a = 0 \/ a = -1.
+intros.
+romega with *.
+Qed.
+
+(* zify_nat *)
+
+Goal forall m: nat, (m<2)%nat -> (0<= m+m <=2)%nat.
+intros.
+romega with *.
+Qed.
+
+Goal forall m:nat, (m<1)%nat -> (m=0)%nat.
+intros.
+romega with *.
+Qed.
+
+Goal forall m: nat, (m<=100)%nat -> (0<= m+m <=200)%nat.
+intros.
+romega with *.
+Qed.
+(* 2000 instead of 200: works, but quite slow *)
+
+Goal forall m: nat, (m*m>=0)%nat.
+intros.
+romega with *.
+Qed.
+
+(* zify_positive *)
+
+Goal forall m: positive, (m<2)%positive -> (2 <= m+m /\ m+m <= 2)%positive.
+intros.
+romega with *.
+Qed.
+
+Goal forall m:positive, (m<2)%positive -> (m=1)%positive.
+intros.
+romega with *.
+Qed.
+
+Goal forall m: positive, (m<=1000)%positive -> (2<=m+m/\m+m <=2000)%positive.
+intros.
+romega with *.
+Qed.
+
+Goal forall m: positive, (m*m>=1)%positive.
+intros.
+romega with *.
+Qed.
+
+(* zify_N *)
+
+Goal forall m:N, (m<2)%N -> (0 <= m+m /\ m+m <= 2)%N.
+intros.
+romega with *.
+Qed.
+
+Goal forall m:N, (m<1)%N -> (m=0)%N.
+intros.
+romega with *.
+Qed.
+
+Goal forall m:N, (m<=1000)%N -> (0<=m+m/\m+m <=2000)%N.
+intros.
+romega with *.
+Qed.
+
+Goal forall m:N, (m*m>=0)%N.
+intros.
+romega with *.
+Qed.
+
+(* mix of datatypes *)
+
+Goal forall p, Z_of_N (N_of_nat (nat_of_N (Npos p))) = Zpos p.
+intros.
+romega with *.
+Qed.
+
+
diff --git a/test-suite/success/apply.v b/test-suite/success/apply.v
index 4f260696..fcce68b9 100644
--- a/test-suite/success/apply.v
+++ b/test-suite/success/apply.v
@@ -7,8 +7,197 @@ assumption.
Qed.
Require Import ZArith.
-Open Scope Z_scope.
-Goal forall x y z, ~ z <= 0 -> x * z < y * z -> x <= y.
+Goal (forall x y z, ~ z <= 0 -> x * z < y * z -> x <= y)%Z.
intros; apply Znot_le_gt, Zgt_lt in H.
apply Zmult_lt_reg_r, Zlt_le_weak in H0; auto.
Qed.
+
+(* Check if it unfolds when there are not enough premises *)
+
+Goal forall n, n = S n -> False.
+intros.
+apply n_Sn in H.
+assumption.
+Qed.
+
+(* Check naming in with bindings; printing used to be inconsistent before *)
+(* revision 9450 *)
+
+Notation S':=S (only parsing).
+Goal (forall S, S = S' S) -> (forall S, S = S' S).
+intros.
+apply H with (S0 := S).
+Qed.
+
+(* Check inference of implicit arguments in bindings *)
+
+Goal exists y : nat -> Type, y 0 = y 0.
+exists (fun x => True).
+trivial.
+Qed.
+
+(* Check universe handling in typed unificationn *)
+
+Definition E := Type.
+Goal exists y : E, y = y.
+exists Prop.
+trivial.
+Qed.
+
+Variable Eq : Prop = (Prop -> Prop) :> E.
+Goal Prop.
+rewrite Eq.
+Abort.
+
+(* Check insertion of coercions in bindings *)
+
+Coercion eq_true : bool >-> Sortclass.
+Goal exists A:Prop, A = A.
+exists true.
+trivial.
+Qed.
+
+(* Check use of unification of bindings types in specialize *)
+
+Variable P : nat -> Prop.
+Variable L : forall (l : nat), P l -> P l.
+Goal P 0 -> True.
+intros.
+specialize L with (1:=H).
+Abort.
+Reset P.
+
+(* Two examples that show that hnf_constr is used when unifying types
+ of bindings (a simplification of a script from Field_Theory) *)
+
+Require Import List.
+Open Scope list_scope.
+Fixpoint P (l : list nat) : Prop :=
+ match l with
+ | nil => True
+ | e1 :: nil => e1 = e1
+ | e1 :: l1 => e1 = e1 /\ P l1
+ end.
+Variable L : forall n l, P (n::l) -> P l.
+
+Goal forall (x:nat) l, P (x::l) -> P l.
+intros.
+apply L with (1:=H).
+Qed.
+
+Goal forall (x:nat) l, match l with nil => x=x | _::_ => x=x /\ P l end -> P l.
+intros.
+apply L with (1:=H).
+Qed.
+
+(* The following call to auto fails if the type of the clause
+ associated to the H is not beta-reduced [but apply H works]
+ (a simplification of a script from FSetAVL) *)
+
+Definition apply (f:nat->Prop) := forall x, f x.
+Goal apply (fun n => n=0) -> 1=0.
+intro H.
+auto.
+Qed.
+
+(* The following fails if the coercion Zpos is not introduced around p
+ before trying a subterm that matches the left-hand-side of the equality
+ (a simplication of an example taken from Nijmegen/QArith) *)
+
+Require Import ZArith.
+Coercion Zpos : positive >-> Z.
+Variable f : Z -> Z -> Z.
+Variable g : forall q1 q2 p : Z, f (f q1 p) (f q2 p) = Z0.
+Goal forall p q1 q2, f (f q1 (Zpos p)) (f q2 (Zpos p)) = Z0.
+intros; rewrite g with (p:=p).
+reflexivity.
+Qed.
+
+(* A funny example where the behavior differs depending on which of a
+ multiple solution to a unification problem is chosen (an instance
+ of this case can be found in the proof of Buchberger.BuchRed.nf_divp) *)
+
+Definition succ x := S x.
+Goal forall (I : nat -> Set) (P : nat -> Prop) (Q : forall n:nat, I n -> Prop),
+ (forall x y, P x -> Q x y) ->
+ (forall x, P (S x)) -> forall y: I (S 0), Q (succ 0) y.
+intros.
+apply H with (y:=y).
+(* [x] had two possible instances: [S 0], coming from unifying the
+ type of [y] with [I ?n] and [succ 0] coming from the unification with
+ the goal; only the first one allows to make the next apply (which
+ does not work modulo delta) working *)
+apply H0.
+Qed.
+
+(* A similar example with a arbitrary long conversion between the two
+ possible instances *)
+
+Fixpoint compute_succ x :=
+ match x with O => S 0 | S n => S (compute_succ n) end.
+
+Goal forall (I : nat -> Set) (P : nat -> Prop) (Q : forall n:nat, I n -> Prop),
+ (forall x y, P x -> Q x y) ->
+ (forall x, P (S x)) -> forall y: I (S 100), Q (compute_succ 100) y.
+intros.
+apply H with (y:=y).
+apply H0.
+Qed.
+
+(* Another example with multiple convertible solutions to the same
+ metavariable (extracted from Algebra.Hom_module.Hom_module, 10th
+ subgoal which precisely fails) *)
+
+Definition ID (A:Type) := A.
+Goal forall f:Type -> Type,
+ forall (P : forall A:Type, A -> Prop),
+ (forall (B:Type) x, P (f B) x -> P (f B) x) ->
+ (forall (A:Type) x, P (f (f A)) x) ->
+ forall (A:Type) (x:f (f A)), P (f (ID (f A))) x.
+intros.
+apply H.
+(* The parameter [B] had two possible instances: [ID (f A)] by direct
+ unification and [f A] by unification of the type of [x]; only the
+ first choice makes the next command fail, as it was
+ (unfortunately?) in Hom_module *)
+try apply H.
+unfold ID; apply H0.
+Qed.
+
+(* Test coercion below product and on non meta-free terms in with bindings *)
+(* Cf wishes #1408 from E. Makarov *)
+
+Parameter bool_Prop :> bool -> Prop.
+Parameter r : bool -> bool -> bool.
+Axiom ax : forall (A : Set) (R : A -> A -> Prop) (x y : A), R x y.
+
+Theorem t : r true false.
+apply ax with (R := r).
+Qed.
+
+(* Check verification of type at unification (submitted by Stéphane Lengrand):
+ without verification, the first "apply" works what leads to the incorrect
+ instantiation of x by Prop *)
+
+Theorem u : ~(forall x:Prop, ~x).
+unfold not.
+intro.
+eapply H.
+apply (forall B:Prop,B->B) || (instantiate (1:=True); exact I).
+Defined.
+
+(* Fine-tuning coercion insertion in presence of unfolding (bug #1883) *)
+
+Parameter name : Set.
+Definition atom := name.
+
+Inductive exp : Set :=
+ | var : atom -> exp.
+
+Coercion var : atom >-> exp.
+
+Axiom silly_axiom : forall v : exp, v = v -> False.
+
+Lemma silly_lemma : forall x : atom, False.
+intros x.
+apply silly_axiom with (v := x). (* fails *)
diff --git a/test-suite/success/cc.v b/test-suite/success/cc.v
index fecc8977..94d827fd 100644
--- a/test-suite/success/cc.v
+++ b/test-suite/success/cc.v
@@ -78,6 +78,14 @@ intros.
congruence.
Qed.
+(* example with implications *)
+
+Theorem arrow : forall (A B: Prop) (C D:Set) , A=B -> C=D ->
+(A -> C) = (B -> D).
+congruence.
+Qed.
+
+
Set Implicit Arguments.
Parameter elt: Set.
@@ -94,5 +102,6 @@ Proof.
auto.
Qed.
+
\ No newline at end of file
diff --git a/test-suite/success/change.v b/test-suite/success/change.v
new file mode 100644
index 00000000..cea01712
--- /dev/null
+++ b/test-suite/success/change.v
@@ -0,0 +1,6 @@
+(* A few tests of the syntax of clauses and of the interpretation of change *)
+
+Goal let a := 0+0 in a=a.
+intro.
+change 0 in (value of a).
+change ((fun A:Type => A) nat) in (type of a).
diff --git a/test-suite/success/clear.v b/test-suite/success/clear.v
index 444146f7..8169361c 100644
--- a/test-suite/success/clear.v
+++ b/test-suite/success/clear.v
@@ -1,6 +1,15 @@
Goal forall x:nat, (forall x, x=0 -> True)->True.
intros; eapply H.
instantiate (1:=(fun y => _) (S x)).
- simpl.
- clear x || trivial.
+ simpl.
+ clear x. trivial.
Qed.
+
+Goal forall y z, (forall x:nat, x=y -> True) -> y=z -> True.
+ intros; eapply H.
+ rename z into z'.
+ clear H0.
+ clear z'.
+ reflexivity.
+Qed.
+
diff --git a/test-suite/success/conv_pbs.v b/test-suite/success/conv_pbs.v
new file mode 100644
index 00000000..062c3ee5
--- /dev/null
+++ b/test-suite/success/conv_pbs.v
@@ -0,0 +1,223 @@
+(* A bit complex but realistic example whose last fixpoint definition
+ used to fail in 8.1 because of wrong environment in conversion
+ problems (see revision 9664) *)
+
+Require Import List.
+Require Import Arith.
+
+Parameter predicate : Set.
+Parameter function : Set.
+Definition variable := nat.
+Definition x0 := 0.
+Definition var_eq_dec := eq_nat_dec.
+
+Inductive term : Set :=
+ | App : function -> term -> term
+ | Var : variable -> term.
+
+Definition atom := (predicate * term)%type.
+
+Inductive formula : Set :=
+ | Atom : atom -> formula
+ | Imply : formula -> formula -> formula
+ | Forall : variable -> formula -> formula.
+
+Notation "A --> B" := (Imply A B) (at level 40).
+
+Definition substitution range := list (variable * range).
+
+Fixpoint remove_assoc (A:Set)(x:variable)(rho: substitution A){struct rho}
+ : substitution A :=
+ match rho with
+ | nil => rho
+ | (y,t) :: rho => if var_eq_dec x y then remove_assoc A x rho
+ else (y,t) :: remove_assoc A x rho
+ end.
+
+Fixpoint assoc (A:Set)(x:variable)(rho:substitution A){struct rho}
+ : option A :=
+ match rho with
+ | nil => None
+ | (y,t) :: rho => if var_eq_dec x y then Some t
+ else assoc A x rho
+ end.
+
+Fixpoint subst_term (rho:substitution term)(t:term){struct t} : term :=
+ match t with
+ | Var x => match assoc _ x rho with
+ | Some a => a
+ | None => Var x
+ end
+ | App f t' => App f (subst_term rho t')
+ end.
+
+Fixpoint subst_formula (rho:substitution term)(A:formula){struct A}:formula :=
+ match A with
+ | Atom (p,t) => Atom (p, subst_term rho t)
+ | A --> B => subst_formula rho A --> subst_formula rho B
+ | Forall y A => Forall y (subst_formula (remove_assoc _ y rho) A)
+ (* assume t closed *)
+ end.
+
+Definition subst A x t := subst_formula ((x,t):: nil) A.
+
+Record Kripke : Type := {
+ worlds: Set;
+ wle : worlds -> worlds -> Type;
+ wle_refl : forall w, wle w w ;
+ wle_trans : forall w w' w'', wle w w' -> wle w' w'' -> wle w w'';
+ domain : Set;
+ vars : variable -> domain;
+ funs : function -> domain -> domain;
+ atoms : worlds -> predicate * domain -> Type;
+ atoms_mon : forall w w', wle w w' -> forall P, atoms w P -> atoms w' P
+}.
+
+Section Sem.
+
+Variable K : Kripke.
+
+Fixpoint sem (rho: substitution (domain K))(t:term){struct t} : domain K :=
+ match t with
+ | Var x => match assoc _ x rho with
+ | Some a => a
+ | None => vars K x
+ end
+ | App f t' => funs K f (sem rho t')
+ end.
+
+End Sem.
+
+Notation "w <= w'" := (wle _ w w').
+
+Set Implicit Arguments.
+
+Reserved Notation "w ||- A" (at level 70).
+
+Definition context := list formula.
+
+Variable fresh : variable -> context -> Prop.
+
+Variable fresh_out : context -> variable.
+
+Axiom fresh_out_spec : forall Gamma, fresh (fresh_out Gamma) Gamma.
+
+Axiom fresh_peel : forall x A Gamma, fresh x (A::Gamma) -> fresh x Gamma.
+
+Fixpoint force (K:Kripke)(rho: substitution (domain K))(w:worlds K)(A:formula)
+ {struct A} : Type :=
+ match A with
+ | Atom (p,t) => atoms K w (p, sem K rho t)
+ | A --> B => forall w', w <= w' -> force K rho w' A -> force K rho w' B
+ | Forall x A => forall w', w <= w' -> forall t, force K ((x,t)::remove_assoc _ x rho) w' A
+ end.
+
+Notation "w ||- A" := (force _ nil w A).
+
+Reserved Notation "Gamma |- A" (at level 70).
+Reserved Notation "Gamma ; A |- C" (at level 70, A at next level).
+
+Inductive context_prefix (Gamma:context) : context -> Type :=
+ | CtxPrefixRefl : context_prefix Gamma Gamma
+ | CtxPrefixTrans : forall A Gamma', context_prefix Gamma Gamma' -> context_prefix Gamma (cons A Gamma').
+
+Inductive in_context (A:formula) : list formula -> Prop :=
+ | InAxiom : forall Gamma, in_context A (cons A Gamma)
+ | OmWeak : forall Gamma B, in_context A Gamma -> in_context A (cons B Gamma).
+
+Inductive prove : list formula -> formula -> Type :=
+ | ProofImplyR : forall A B Gamma, prove (cons A Gamma) B
+ -> prove Gamma (A --> B)
+ | ProofForallR : forall x A Gamma, (forall y, fresh y (A::Gamma)
+ -> prove Gamma (subst A x (Var y))) -> prove Gamma (Forall x A)
+ | ProofCont : forall A Gamma Gamma' C, context_prefix (A::Gamma) Gamma'
+ -> (prove_stoup Gamma' A C) -> (Gamma' |- C)
+
+where "Gamma |- A" := (prove Gamma A)
+
+ with prove_stoup : list formula -> formula -> formula -> Type :=
+ | ProofAxiom Gamma C: Gamma ; C |- C
+ | ProofImplyL Gamma C : forall A B, (Gamma |- A)
+ -> (prove_stoup Gamma B C) -> (prove_stoup Gamma (A --> B) C)
+ | ProofForallL Gamma C : forall x t A, (prove_stoup Gamma (subst A x t) C)
+ -> (prove_stoup Gamma (Forall x A) C)
+
+where " Gamma ; B |- A " := (prove_stoup Gamma B A).
+
+Axiom context_prefix_trans :
+ forall Gamma Gamma' Gamma'',
+ context_prefix Gamma Gamma'
+ -> context_prefix Gamma' Gamma''
+ -> context_prefix Gamma Gamma''.
+
+Axiom Weakening :
+ forall Gamma Gamma' A,
+ context_prefix Gamma Gamma' -> Gamma |- A -> Gamma' |- A.
+
+Axiom universal_weakening :
+ forall Gamma Gamma', context_prefix Gamma Gamma'
+ -> forall P, Gamma |- Atom P -> Gamma' |- Atom P.
+
+Canonical Structure Universal := Build_Kripke
+ context
+ context_prefix
+ CtxPrefixRefl
+ context_prefix_trans
+ term
+ Var
+ App
+ (fun Gamma P => Gamma |- Atom P)
+ universal_weakening.
+
+Axiom subst_commute :
+ forall A rho x t,
+ subst_formula ((x,t)::rho) A = subst (subst_formula rho A) x t.
+
+Axiom subst_formula_atom :
+ forall rho p t,
+ Atom (p, sem _ rho t) = subst_formula rho (Atom (p,t)).
+
+Fixpoint universal_completeness (Gamma:context)(A:formula){struct A}
+ : forall rho:substitution term,
+ force _ rho Gamma A -> Gamma |- subst_formula rho A
+ :=
+ match A
+ return forall rho, force _ rho Gamma A
+ -> Gamma |- subst_formula rho A
+ with
+ | Atom (p,t) => fun rho H => eq_rect _ (fun A => Gamma |- A) H _ (subst_formula_atom rho p t)
+ | A --> B => fun rho HImplyAB =>
+ let A' := subst_formula rho A in
+ ProofImplyR (universal_completeness (A'::Gamma) B rho
+ (HImplyAB (A'::Gamma)(CtxPrefixTrans A' (CtxPrefixRefl Gamma))
+ (universal_completeness_stoup A rho (fun C Gamma' Hle p
+ => ProofCont Hle p))))
+ | Forall x A => fun rho HForallA
+ => ProofForallR x (fun y Hfresh
+ => eq_rect _ _ (universal_completeness Gamma A _
+ (HForallA Gamma (CtxPrefixRefl Gamma)(Var y))) _ (subst_commute _ _ _ _ ))
+ end
+with universal_completeness_stoup (Gamma:context)(A:formula){struct A}
+ : forall rho, (forall C Gamma', context_prefix Gamma Gamma'
+ -> Gamma' ; subst_formula rho A |- C -> Gamma' |- C)
+ -> force _ rho Gamma A
+ :=
+ match A return forall rho,
+ (forall C Gamma', context_prefix Gamma Gamma'
+ -> Gamma' ; subst_formula rho A |- C
+ -> Gamma' |- C)
+ -> force _ rho Gamma A
+ with
+ | Atom (p,t) as C => fun rho H
+ => H _ Gamma (CtxPrefixRefl Gamma)(ProofAxiom _ _)
+ | A --> B => fun rho H => fun Gamma' Hle HA
+ => universal_completeness_stoup B rho (fun C Gamma'' Hle' p
+ => H C Gamma'' (context_prefix_trans Hle Hle')
+ (ProofImplyL (Weakening Hle' (universal_completeness Gamma' A rho HA)) p))
+ | Forall x A => fun rho H => fun Gamma' Hle t
+ => (universal_completeness_stoup A ((x,t)::remove_assoc _ x rho)
+ (fun C Gamma'' Hle' p =>
+ H C Gamma'' (context_prefix_trans Hle Hle')
+ (ProofForallL x t (subst_formula (remove_assoc _ x rho) A)
+ (eq_rect _ (fun D => Gamma'' ; D |- C) p _ (subst_commute _ _ _ _)))))
+ end.
diff --git a/test-suite/success/decl_mode.v b/test-suite/success/decl_mode.v
new file mode 100644
index 00000000..fede31a8
--- /dev/null
+++ b/test-suite/success/decl_mode.v
@@ -0,0 +1,182 @@
+(* \sqrt 2 is irrationnal, (c) 2006 Pierre Corbineau *)
+
+Set Firstorder Depth 1.
+Require Import ArithRing Wf_nat Peano_dec Div2 Even Lt.
+
+Lemma double_div2: forall n, div2 (double n) = n.
+proof.
+ assume n:nat.
+ per induction on n.
+ suppose it is 0.
+ suffices (0=0) to show thesis.
+ thus thesis.
+ suppose it is (S m) and Hrec:thesis for m.
+ have (div2 (double (S m))= div2 (S (S (double m)))).
+ ~= (S (div2 (double m))).
+ thus ~= (S m) by Hrec.
+ end induction.
+end proof.
+Show Script.
+Qed.
+
+Lemma double_inv : forall n m, double n = double m -> n = m .
+proof.
+ let n, m be such that H:(double n = double m).
+have (n = div2 (double n)) by double_div2,H.
+ ~= (div2 (double m)) by H.
+ thus ~= m by double_div2.
+end proof.
+Qed.
+
+Lemma double_mult_l : forall n m, (double (n * m)=n * double m).
+proof.
+ assume n:nat and m:nat.
+ have (double (n * m) = n*m + n * m).
+ ~= (n * (m+m)) by * using ring.
+ thus ~= (n * double m).
+end proof.
+Qed.
+
+Lemma double_mult_r : forall n m, (double (n * m)=double n * m).
+proof.
+ assume n:nat and m:nat.
+ have (double (n * m) = n*m + n * m).
+ ~= ((n + n) * m) by * using ring.
+ thus ~= (double n * m).
+end proof.
+Qed.
+
+Lemma even_is_even_times_even: forall n, even (n*n) -> even n.
+proof.
+ let n be such that H:(even (n*n)).
+ per cases of (even n \/ odd n) by even_or_odd.
+ suppose (odd n).
+ hence thesis by H,even_mult_inv_r.
+ end cases.
+end proof.
+Qed.
+
+Lemma main_thm_aux: forall n,even n ->
+double (double (div2 n *div2 n))=n*n.
+proof.
+ given n such that H:(even n).
+ *** have (double (double (div2 n * div2 n))
+ = double (div2 n) * double (div2 n))
+ by double_mult_l,double_mult_r.
+ thus ~= (n*n) by H,even_double.
+end proof.
+Qed.
+
+Require Omega.
+
+Lemma even_double_n: (forall m, even (double m)).
+proof.
+ assume m:nat.
+ per induction on m.
+ suppose it is 0.
+ thus thesis.
+ suppose it is (S mm) and thesis for mm.
+ then H:(even (S (S (mm+mm)))).
+ have (S (S (mm + mm)) = S mm + S mm) using omega.
+ hence (even (S mm +S mm)) by H.
+ end induction.
+end proof.
+Qed.
+
+Theorem main_theorem: forall n p, n*n=double (p*p) -> p=0.
+proof.
+ assume n0:nat.
+ define P n as (forall p, n*n=double (p*p) -> p=0).
+ claim rec_step: (forall n, (forall m,m<n-> P m) -> P n).
+ let n be such that H:(forall m : nat, m < n -> P m) and p:nat .
+ per cases of ({n=0}+{n<>0}) by eq_nat_dec.
+ suppose H1:(n=0).
+ per cases on p.
+ suppose it is (S p').
+ assume (n * n = double (S p' * S p')).
+ =~ 0 by H1,mult_n_O.
+ ~= (S ( p' + p' * S p' + S p'* S p'))
+ by plus_n_Sm.
+ hence thesis .
+ suppose it is 0.
+ thus thesis.
+ end cases.
+ suppose H1:(n<>0).
+ assume H0:(n*n=double (p*p)).
+ have (even (double (p*p))) by even_double_n .
+ then (even (n*n)) by H0.
+ then H2:(even n) by even_is_even_times_even.
+ then (double (double (div2 n *div2 n))=n*n)
+ by main_thm_aux.
+ ~= (double (p*p)) by H0.
+ then H':(double (div2 n *div2 n)= p*p) by double_inv.
+ have (even (double (div2 n *div2 n))) by even_double_n.
+ then (even (p*p)) by even_double_n,H'.
+ then H3:(even p) by even_is_even_times_even.
+ have (double(double (div2 n * div2 n)) = n*n)
+ by H2,main_thm_aux.
+ ~= (double (p*p)) by H0.
+ ~= (double(double (double (div2 p * div2 p))))
+ by H3,main_thm_aux.
+ then H'':(div2 n * div2 n = double (div2 p * div2 p))
+ by double_inv.
+ then (div2 n < n) by lt_div2,neq_O_lt,H1.
+ then H4:(div2 p=0) by (H (div2 n)),H''.
+ then (double (div2 p) = double 0).
+ =~ p by even_double,H3.
+ thus ~= 0.
+ end cases.
+ end claim.
+ hence thesis by (lt_wf_ind n0 P).
+end proof.
+Qed.
+
+Require Import Reals Field.
+(*Coercion INR: nat >->R.
+Coercion IZR: Z >->R.*)
+
+Open Scope R_scope.
+
+Lemma square_abs_square:
+ forall p,(INR (Zabs_nat p) * INR (Zabs_nat p)) = (IZR p * IZR p).
+proof.
+ assume p:Z.
+ per cases on p.
+ suppose it is (0%Z).
+ thus thesis.
+ suppose it is (Zpos z).
+ thus thesis.
+ suppose it is (Zneg z).
+ have ((INR (Zabs_nat (Zneg z)) * INR (Zabs_nat (Zneg z))) =
+ (IZR (Zpos z) * IZR (Zpos z))).
+ ~= ((- IZR (Zpos z)) * (- IZR (Zpos z))).
+ thus ~= (IZR (Zneg z) * IZR (Zneg z)).
+ end cases.
+end proof.
+Qed.
+
+Definition irrational (x:R):Prop :=
+ forall (p:Z) (q:nat),q<>0%nat -> x<> (IZR p/INR q).
+
+Theorem irrationnal_sqrt_2: irrational (sqrt (INR 2%nat)).
+proof.
+ let p:Z,q:nat be such that H:(q<>0%nat)
+ and H0:(sqrt (INR 2%nat)=(IZR p/INR q)).
+ have H_in_R:(INR q<>0:>R) by H.
+ have triv:((IZR p/INR q* INR q) =IZR p :>R) by * using field.
+ have sqrt2:((sqrt (INR 2%nat) * sqrt (INR 2%nat))= INR 2%nat:>R) by sqrt_def.
+ have (INR (Zabs_nat p * Zabs_nat p)
+ = (INR (Zabs_nat p) * INR (Zabs_nat p)))
+ by mult_INR.
+ ~= (IZR p* IZR p) by square_abs_square.
+ ~= ((IZR p/INR q*INR q)*(IZR p/INR q*INR q)) by triv. (* we have to factor because field is too weak *)
+ ~= ((IZR p/INR q)*(IZR p/INR q)*(INR q*INR q)) using ring.
+ ~= (sqrt (INR 2%nat) * sqrt (INR 2%nat)*(INR q*INR q)) by H0.
+ ~= (INR (2%nat * (q*q))) by sqrt2,mult_INR.
+ then (Zabs_nat p * Zabs_nat p = 2* (q * q))%nat.
+ ~= ((q*q)+(q*q))%nat.
+ ~= (Div2.double (q*q)).
+ then (q=0%nat) by main_theorem.
+ hence thesis by H.
+end proof.
+Qed.
diff --git a/test-suite/success/dependentind.v b/test-suite/success/dependentind.v
new file mode 100644
index 00000000..48255386
--- /dev/null
+++ b/test-suite/success/dependentind.v
@@ -0,0 +1,100 @@
+Require Import Coq.Program.Program.
+Set Implicit Arguments.
+Unset Strict Implicit.
+
+Variable A : Set.
+
+Inductive vector : nat -> Type := vnil : vector 0 | vcons : A -> forall n, vector n -> vector (S n).
+
+Goal forall n, forall v : vector (S n), vector n.
+Proof.
+ intros n H.
+ dependent destruction H.
+ assumption.
+Save.
+
+Require Import ProofIrrelevance.
+
+Goal forall n, forall v : vector (S n), exists v' : vector n, exists a : A, v = vcons a v'.
+Proof.
+ intros n v.
+ dependent destruction v.
+ exists v ; exists a.
+ reflexivity.
+Save.
+
+(* Extraction Unnamed_thm. *)
+
+Inductive type : Type :=
+| base : type
+| arrow : type -> type -> type.
+
+Notation " t --> t' " := (arrow t t') (at level 20, t' at next level).
+
+Inductive ctx : Type :=
+| empty : ctx
+| snoc : ctx -> type -> ctx.
+
+Notation " Γ , τ " := (snoc Γ τ) (at level 25, t at next level, left associativity).
+
+Fixpoint conc (Γ Δ : ctx) : ctx :=
+ match Δ with
+ | empty => Γ
+ | snoc Δ' x => snoc (conc Γ Δ') x
+ end.
+
+Notation " Γ ; Δ " := (conc Γ Δ) (at level 25, left associativity).
+
+Inductive term : ctx -> type -> Type :=
+| ax : forall Γ τ, term (Γ, τ) τ
+| weak : forall Γ τ, term Γ τ -> forall τ', term (Γ, τ') τ
+| abs : forall Γ τ τ', term (Γ , τ) τ' -> term Γ (τ --> τ')
+| app : forall Γ τ τ', term Γ (τ --> τ') -> term Γ τ -> term Γ τ'.
+
+Lemma weakening : forall Γ Δ τ, term (Γ ; Δ) τ ->
+ forall τ', term (Γ , τ' ; Δ) τ.
+Proof with simpl in * ; auto ; simpl_depind.
+ intros Γ Δ τ H.
+
+ dependent induction H.
+
+ destruct Δ...
+ apply weak ; apply ax.
+
+ apply ax.
+
+ destruct Δ...
+ specialize (IHterm Γ empty)...
+ apply weak...
+
+ apply weak...
+
+ destruct Δ...
+ apply weak ; apply abs ; apply H.
+
+ apply abs...
+ specialize (IHterm Γ0 (Δ, t, τ))...
+
+ apply app with Ï„...
+Qed.
+
+Lemma exchange : forall Γ Δ α β τ, term (Γ, α, β ; Δ) τ -> term (Γ, β, α ; Δ) τ.
+Proof with simpl in * ; simpl_depind ; auto.
+ intros until 1.
+ dependent induction H.
+
+ destruct Δ...
+ apply weak ; apply ax.
+
+ apply ax.
+
+ destruct Δ...
+ pose (weakening (Γ:=Γ0) (Δ:=(empty, α)))...
+
+ apply weak...
+
+ apply abs...
+ specialize (IHterm Γ0 α β (Δ, τ))...
+
+ eapply app with Ï„...
+Save.
diff --git a/test-suite/success/destruct.v b/test-suite/success/destruct.v
index 9f938e10..5aa78816 100644
--- a/test-suite/success/destruct.v
+++ b/test-suite/success/destruct.v
@@ -23,3 +23,35 @@ set (b := true) in *.
try destruct b.
Abort.
+(* Used to fail with error "n is used in conclusion" before revision 9447 *)
+
+Goal forall n, n = S n.
+induction S.
+Abort.
+
+(* Check that elimination with remaining evars do not raise an bad
+ error message *)
+
+Theorem Refl : forall P, P <-> P. tauto. Qed.
+Goal True.
+case Refl || ecase Refl.
+Abort.
+
+
+(* Submitted by B. Baydemir (bug #1882) *)
+
+Require Import List.
+
+Definition alist R := list (nat * R)%type.
+
+Section Properties.
+ Variables A : Type.
+ Variables a : A.
+ Variables E : alist A.
+
+ Lemma silly : E = E.
+ Proof.
+ clear. induction E. (* this fails. *)
+ Abort.
+
+End Properties.
diff --git a/test-suite/success/evars.v b/test-suite/success/evars.v
index ad69ced1..082cbfbe 100644
--- a/test-suite/success/evars.v
+++ b/test-suite/success/evars.v
@@ -68,9 +68,145 @@ Proof. trivial. Qed.
Hint Resolve contradiction.
Goal False.
eauto.
+Abort.
(* This used to fail in V8.1beta because first-order unification was
used before using type information *)
Check (exist _ O (refl_equal 0) : {n:nat|n=0}).
Check (exist _ O I : {n:nat|True}).
+
+(* An example (initially from Marseille/Fairisle) that involves an evar with
+ different solutions (Input, Output or bool) that may or may not be
+ considered distinct depending on which kind of conversion is used *)
+
+Section A.
+Definition STATE := (nat * bool)%type.
+Let Input := bool.
+Let Output := bool.
+Parameter Out : STATE -> Output.
+Check fun (s : STATE) (reg : Input) => reg = Out s.
+End A.
+
+(* The return predicate found should be: "in _=U return U" *)
+(* (feature already available in V8.0) *)
+
+Definition g (T1 T2:Type) (x:T1) (e:T1=T2) : T2 :=
+ match e with
+ | refl_equal => x
+ end.
+
+(* An example extracted from FMapAVL which (may) test restriction on
+ evars problems of the form ?n[args1]=?n[args2] with distinct args1
+ and args2 *)
+
+Set Implicit Arguments.
+Parameter t:Set->Set.
+Parameter map:forall elt elt' : Set, (elt -> elt') -> t elt -> t elt'.
+Parameter avl: forall elt : Set, t elt -> Prop.
+Parameter bst: forall elt : Set, t elt -> Prop.
+Parameter map_avl: forall (elt elt' : Set) (f : elt -> elt') (m : t elt),
+ avl m -> avl (map f m).
+Parameter map_bst: forall (elt elt' : Set) (f : elt -> elt') (m : t elt),
+ bst m -> bst (map f m).
+Record bbst (elt:Set) : Set :=
+ Bbst {this :> t elt; is_bst : bst this; is_avl: avl this}.
+Definition t' := bbst.
+Section B.
+Variables elt elt': Set.
+Definition map' f (m:t' elt) : t' elt' :=
+ Bbst (map_bst f m.(is_bst)) (map_avl f m.(is_avl)).
+End B.
+Unset Implicit Arguments.
+
+(* An example from Lexicographic_Exponentiation that tests the
+ contraction of reducible fixpoints in type inference *)
+
+Require Import List.
+Check (fun (A:Set) (a b x:A) (l:list A)
+ (H : l ++ cons x nil = cons b (cons a nil)) =>
+ app_inj_tail l (cons b nil) _ _ H).
+
+(* An example from NMake (simplified), that uses restriction in solve_refl *)
+
+Parameter h:(nat->nat)->(nat->nat).
+Fixpoint G p cont {struct p} :=
+ h (fun n => match p with O => cont | S p => G p cont end n).
+
+(* An example from Bordeaux/Cantor that applies evar restriction
+ below a binder *)
+
+Require Import Relations.
+Parameter lex : forall (A B : Set), (forall (a1 a2:A), {a1=a2}+{a1<>a2})
+-> relation A -> relation B -> A * B -> A * B -> Prop.
+Check
+ forall (A B : Set) eq_A_dec o1 o2,
+ antisymmetric A o1 -> transitive A o1 -> transitive B o2 ->
+ transitive _ (lex _ _ eq_A_dec o1 o2).
+
+(* Another example from Julien Forest that tests unification below binders *)
+
+Require Import List.
+Set Implicit Arguments.
+Parameter
+ merge : forall (A B : Set) (eqA : forall (a1 a2 : A), {a1=a2}+{a1<>a2})
+ (eqB : forall (b1 b2 : B), {b1=b2}+{b1<>b2})
+ (partial_res l : list (A*B)), option (list (A*B)).
+Axiom merge_correct :
+ forall (A B : Set) eqA eqB (l1 l2 : list (A*B)),
+ (forall a2 b2 c2, In (a2,b2) l2 -> In (a2,c2) l2 -> b2 = c2) ->
+ match merge eqA eqB l1 l2 with _ => True end.
+Unset Implicit Arguments.
+
+(* An example from Bordeaux/Additions that tests restriction below binders *)
+
+Section Additions_while.
+
+Variable A : Set.
+Variables P Q : A -> Prop.
+Variable le : A -> A -> Prop.
+Hypothesis Q_dec : forall s : A, P s -> {Q s} + {~ Q s}.
+Hypothesis le_step : forall s : A, ~ Q s -> P s -> {s' | P s' /\ le s' s}.
+Hypothesis le_wf : well_founded le.
+
+Lemma loopexec : forall s : A, P s -> {s' : A | P s' /\ Q s'}.
+refine
+ (well_founded_induction_type le_wf (fun s => _ -> {s' : A | _ /\ _})
+ (fun s hr i =>
+ match Q_dec s i with
+ | left _ => _
+ | right _ =>
+ match le_step s _ _ with
+ | exist s' h' =>
+ match hr s' _ _ with
+ | exist s'' _ => exist _ s'' _
+ end
+ end
+ end)).
+Abort.
+
+End Additions_while.
+
+(* Two examples from G. Melquiond (bugs #1878 and #1884) *)
+
+Parameter F1 G1 : nat -> Prop.
+Goal forall x : nat, F1 x -> G1 x.
+refine (fun x H => proj2 (_ x H)).
+Abort.
+
+Goal forall x : nat, F1 x -> G1 x.
+refine (fun x H => proj2 (_ x H) _).
+Abort.
+
+(* Remark: the following example does not succeed any longer in 8.2 because,
+ the algorithm is more general and does exclude a solution that it should
+ exclude for typing reason. Handling of types and backtracking is still to
+ be done
+
+Section S.
+Variables A B : nat -> Prop.
+Goal forall x : nat, A x -> B x.
+refine (fun x H => proj2 (_ x H) _).
+Abort.
+End S.
+*)
diff --git a/test-suite/success/extraction.v b/test-suite/success/extraction.v
index 0b3060d5..74d87ffa 100644
--- a/test-suite/success/extraction.v
+++ b/test-suite/success/extraction.v
@@ -84,7 +84,7 @@ Extraction test12.
(* type test12 = (__ -> __ -> __) -> __ *)
-Definition test13 := match left True I with
+Definition test13 := match @left True True I with
| left x => 1
| right x => 0
end.
diff --git a/test-suite/success/fix.v b/test-suite/success/fix.v
index f4a4d36d..78b01f3e 100644
--- a/test-suite/success/fix.v
+++ b/test-suite/success/fix.v
@@ -1,10 +1,3 @@
-(************************************************************************)
-(* v * The Coq Proof Assistant / The Coq Development Team *)
-(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
-(* \VV/ **************************************************************)
-(* // * This file is distributed under the terms of the *)
-(* * GNU Lesser General Public License Version 2.1 *)
-(************************************************************************)
(* Ancien bug signale par Laurent Thery sur la condition de garde *)
Require Import Bool.
@@ -50,3 +43,55 @@ Fixpoint maxVar (e : rExpr) : rNat :=
| rNode n p q => rmax (maxVar p) (maxVar q)
end.
+(* Check bug #1491 *)
+
+Require Import Streams.
+
+Definition decomp (s:Stream nat) : Stream nat :=
+ match s with Cons _ s => s end.
+
+CoFixpoint bx0 : Stream nat := Cons 0 bx1
+with bx1 : Stream nat := Cons 1 bx0.
+
+Lemma bx0bx : decomp bx0 = bx1.
+simpl. (* used to return bx0 in V8.1 and before instead of bx1 *)
+reflexivity.
+Qed.
+
+(* Check mutually inductive statements *)
+
+Require Import ZArith_base Omega.
+Open Scope Z_scope.
+
+Inductive even: Z -> Prop :=
+| even_base: even 0
+| even_succ: forall n, odd (n - 1) -> even n
+with odd: Z -> Prop :=
+| odd_succ: forall n, even (n - 1) -> odd n.
+
+Lemma even_pos_odd_pos: forall n, even n -> n >= 0
+with odd_pos_even_pos : forall n, odd n -> n >= 1.
+Proof.
+ intros.
+ destruct H.
+ omega.
+ apply odd_pos_even_pos in H.
+ omega.
+ intros.
+ destruct H.
+ apply even_pos_odd_pos in H.
+ omega.
+Qed.
+
+CoInductive a : Prop := acons : b -> a
+with b : Prop := bcons : a -> b.
+
+Lemma a1 : a
+with b1 : b.
+Proof.
+apply acons.
+assumption.
+
+apply bcons.
+assumption.
+Qed.
diff --git a/test-suite/success/hyps_inclusion.v b/test-suite/success/hyps_inclusion.v
new file mode 100644
index 00000000..21bfc075
--- /dev/null
+++ b/test-suite/success/hyps_inclusion.v
@@ -0,0 +1,32 @@
+(* Simplified example for bug #1325 *)
+
+(* Explanation: the proof engine see section variables as goal
+ variables; especially, it can change their types so that, at
+ type-checking, the section variables are not recognized
+ (Typeops.check_hyps_inclusion raises "types do no match"). It
+ worked before the introduction of polymorphic inductive types because
+ tactics were using Typing.type_of and not Typeops.typing; the former
+ was not checking hyps inclusion so that the discrepancy in the types
+ of section variables seen as goal variables was not a problem (at the
+ end, when the proof is completed, the section variable recovers its
+ original type and all is correct for Typeops) *)
+
+Section A.
+Variable H:not True.
+Lemma f:nat->nat. destruct H. exact I. Defined.
+Goal f 0=f 1.
+red in H.
+(* next tactic was failing wrt bug #1325 because type-checking the goal
+ detected a syntactically different type for the section variable H *)
+case 0.
+Reset A.
+
+(* Variant with polymorphic inductive types for bug #1325 *)
+
+Section A.
+Variable H:not True.
+Inductive I (n:nat) : Type := C : H=H -> I n.
+Goal I 0.
+red in H.
+case 0.
+Reset A.
diff --git a/test-suite/success/implicit.v b/test-suite/success/implicit.v
index 47c58f04..9034d6a6 100644
--- a/test-suite/success/implicit.v
+++ b/test-suite/success/implicit.v
@@ -36,3 +36,13 @@ Check (fun x => @ rhs _ _ (f x)).
Fixpoint g n := match n with O => true | S n => g n end.
Inductive P n : nat -> Prop := c : P n n.
+
+(* Avoid evars in the computation of implicit arguments (cf r9827) *)
+
+Require Import List.
+
+Fixpoint plus n m {struct n} :=
+ match n with
+ | 0 => m
+ | S p => S (plus p m)
+ end.
diff --git a/test-suite/success/ltac.v b/test-suite/success/ltac.v
index 3f25f703..757cf6a4 100644
--- a/test-suite/success/ltac.v
+++ b/test-suite/success/ltac.v
@@ -173,5 +173,50 @@ Abort.
empty args *)
Goal True.
-match None with @None => exact I end.
+match constr:@None with @None => exact I end.
Abort.
+
+(* Check second-order pattern unification *)
+
+Ltac to_exist :=
+ match goal with
+ |- forall x y, @?P x y =>
+ let Q := eval lazy beta in (exists x, forall y, P x y) in
+ assert (Q->Q)
+ end.
+
+Goal forall x y : nat, x = y.
+to_exist. exact (fun H => H).
+Abort.
+
+(* Used to fail in V8.1 *)
+
+Tactic Notation "test" constr(t) integer(n) :=
+ set (k := t) in |- * at n.
+
+Goal forall x : nat, x = 1 -> x + x + x = 3.
+intros x H.
+test x 2.
+Abort.
+
+(* Utilisation de let rec sans arguments *)
+
+Ltac is :=
+ let rec i := match goal with |- ?A -> ?B => intro; i | _ => idtac end in
+ i.
+
+Goal True -> True -> True.
+is.
+exact I.
+Abort.
+
+(* Interférence entre espaces des noms *)
+
+Ltac O := intro.
+Ltac Z1 t := set (x:=t).
+Ltac Z2 t := t.
+Goal True -> True.
+Z1 O.
+Z2 ltac:O.
+exact I.
+Qed.
diff --git a/test-suite/success/options.v b/test-suite/success/options.v
index bb678150..f43a4694 100644
--- a/test-suite/success/options.v
+++ b/test-suite/success/options.v
@@ -20,7 +20,7 @@ Parameter i : bool -> nat.
Coercion i : bool >-> nat.
Add Printing Coercion i.
Remove Printing Coercion i.
-Test Printing Coercion i.
+Test Printing Coercion for i.
Test Printing Let.
Test Printing If.
diff --git a/test-suite/success/parsing.v b/test-suite/success/parsing.v
new file mode 100644
index 00000000..d1b679d5
--- /dev/null
+++ b/test-suite/success/parsing.v
@@ -0,0 +1,8 @@
+Section A.
+Notation "*" := O (at level 8).
+Notation "**" := O (at level 99).
+Notation "***" := O (at level 9).
+End A.
+Notation "*" := O (at level 8).
+Notation "**" := O (at level 99).
+Notation "***" := O (at level 9).
diff --git a/test-suite/success/pattern.v b/test-suite/success/pattern.v
new file mode 100644
index 00000000..28d0bd55
--- /dev/null
+++ b/test-suite/success/pattern.v
@@ -0,0 +1,7 @@
+(* Test pattern with dependent occurrences; Note that it does not
+ behave as the succession of three generalize because each
+ quantification introduces new occurrences that are automatically
+ abstracted with the numbering still based on the original statement *)
+
+Goal (id true,id false)=(id true,id true).
+generalize bool at 2 4 6 8 10 as B, true at 3 as tt, false as ff.
diff --git a/test-suite/success/refine.v b/test-suite/success/refine.v
index 4346ce9a..4b636618 100644
--- a/test-suite/success/refine.v
+++ b/test-suite/success/refine.v
@@ -87,3 +87,33 @@ refine
| exist _ _ => _
end).
Abort.
+
+
+(* Use to fail because sigma was not propagated to get_type_of *)
+(* Revealed by r9310, fixed in r9359 *)
+
+Goal
+ forall f : forall a (H:a=a), Prop,
+ (forall a (H:a = a :> nat), f a H -> True /\ True) ->
+ True.
+intros.
+refine (@proj1 _ _ (H 0 _ _)).
+Abort.
+
+(* Use to fail because let-in with metas in the body where rejected
+ because a priori considered as dependent *)
+
+Require Import Peano_dec.
+
+Definition fact_F :
+ forall (n:nat),
+ (forall m, m<n -> nat) ->
+ nat.
+refine
+ (fun n fact_rec =>
+ if eq_nat_dec n 0 then
+ 1
+ else
+ let fn := fact_rec (n-1) _ in
+ n * fn).
+Abort.
diff --git a/test-suite/success/rewrite.v b/test-suite/success/rewrite.v
index 9629b213..86e55922 100644
--- a/test-suite/success/rewrite.v
+++ b/test-suite/success/rewrite.v
@@ -17,3 +17,24 @@ intros n n' l l'.
dependent rewrite (ax n n' l l').
split; reflexivity.
Qed.
+
+(* Used to raise an anomaly instead of an error in 8.1 *)
+(* Submitted by Y. Makarov *)
+
+Parameter N : Set.
+Parameter E : N -> N -> Prop.
+
+Axiom e : forall (A : Set) (EA : A -> A -> Prop) (a : A), EA a a.
+
+Theorem th : forall x : N, E x x.
+intro x. try rewrite e.
+Abort.
+
+(* Behavior of rewrite wrt conversion *)
+
+Require Import Arith.
+
+Goal forall n, 0 + n = n -> True.
+intros n H.
+rewrite plus_0_l in H.
+Abort.
diff --git a/test-suite/success/setoid_test.v b/test-suite/success/setoid_test.v
index dd1022f0..f49f58e5 100644
--- a/test-suite/success/setoid_test.v
+++ b/test-suite/success/setoid_test.v
@@ -18,7 +18,7 @@ Definition same (s t : set) : Prop := forall a : A, In a s <-> In a t.
Lemma setoid_set : Setoid_Theory set same.
-unfold same in |- *; split.
+unfold same in |- *; split ; red.
red in |- *; auto.
red in |- *.
@@ -104,3 +104,15 @@ setoid_rewrite <- H.
trivial.
Qed.
+(* Unifying the domain up to delta-conversion (example from emakarov) *)
+
+Definition id: Set -> Set := fun A => A.
+Definition rel : forall A : Set, relation (id A) := @eq.
+Definition f: forall A : Set, A -> A := fun A x => x.
+
+Add Relation (id A) (rel A) as eq_rel.
+
+Add Morphism (@f A) : f_morph.
+Proof.
+unfold rel, f. trivial.
+Qed.
diff --git a/test-suite/success/setoid_test2.v b/test-suite/success/setoid_test2.v
index bac1cf14..34fff9d1 100644
--- a/test-suite/success/setoid_test2.v
+++ b/test-suite/success/setoid_test2.v
@@ -120,6 +120,8 @@ Axiom eqS1: S1 -> S1 -> Prop.
Axiom SetoidS1 : Setoid_Theory S1 eqS1.
Add Setoid S1 eqS1 SetoidS1 as S1setoid.
+Instance eqS1_default : DefaultRelation S1 eqS1.
+
Axiom eqS1': S1 -> S1 -> Prop.
Axiom SetoidS1' : Setoid_Theory S1 eqS1'.
Axiom SetoidS1'_bis : Setoid_Theory S1 eqS1'.
@@ -218,6 +220,8 @@ Axiom eqS1_test8: S1_test8 -> S1_test8 -> Prop.
Axiom SetoidS1_test8 : Setoid_Theory S1_test8 eqS1_test8.
Add Setoid S1_test8 eqS1_test8 SetoidS1_test8 as S1_test8setoid.
+Instance eqS1_test8_default : DefaultRelation S1_test8 eqS1_test8.
+
Axiom f_test8 : S2 -> S1_test8.
Add Morphism f_test8 : f_compat_test8. Admitted.
diff --git a/test-suite/success/setoid_test_function_space.v b/test-suite/success/setoid_test_function_space.v
index 1602991d..ead93d91 100644
--- a/test-suite/success/setoid_test_function_space.v
+++ b/test-suite/success/setoid_test_function_space.v
@@ -26,14 +26,14 @@ Hint Unfold feq. Hint Resolve feq_refl feq_sym feq_trans.
Variable K:(nat -> nat)->Prop.
Variable K_ext:forall a b, (K a)->(a =f b)->(K b).
-Add Relation (fun A B:Type => A -> B) feq
- reflexivity proved by feq_refl
- symmetry proved by feq_sym
- transitivity proved by feq_trans as funsetoid.
+Add Parametric Relation (A B : Type) : (A -> B) (@feq A B)
+ reflexivity proved by (@feq_refl A B)
+ symmetry proved by (@feq_sym A B)
+ transitivity proved by (@feq_trans A B) as funsetoid.
-Add Morphism K with signature feq ==> iff as K_ext1.
+Add Morphism K with signature (@feq nat nat) ==> iff as K_ext1.
intuition. apply (K_ext H0 H).
-intuition. assert (x2 =f x1);auto. apply (K_ext H0 H1).
+intuition. assert (y =f x);auto. apply (K_ext H0 H1).
Qed.
Lemma three:forall n, forall a, (K a)->(a =f (fun m => (a (n+m))))-> (K (fun m
diff --git a/test-suite/success/specialize.v b/test-suite/success/specialize.v
new file mode 100644
index 00000000..4929ae4c
--- /dev/null
+++ b/test-suite/success/specialize.v
@@ -0,0 +1,48 @@
+
+Goal forall a b c : nat, a = b -> b = c -> forall d, a+d=c+d.
+intros.
+
+(* "compatibility" mode: specializing a global name
+ means a kind of generalize *)
+
+specialize trans_equal. intros _.
+specialize trans_equal with (1:=H)(2:=H0). intros _.
+specialize trans_equal with (x:=a)(y:=b)(z:=c). intros _.
+specialize trans_equal with (1:=H)(z:=c). intros _.
+specialize trans_equal with nat a b c. intros _.
+specialize (@trans_equal nat). intros _.
+specialize (@trans_equal _ a b c). intros _.
+specialize (trans_equal (x:=a)). intros _.
+specialize (trans_equal (x:=a)(y:=b)). intros _.
+specialize (trans_equal H H0). intros _.
+specialize (trans_equal H0 (z:=b)). intros _.
+
+(* local "in place" specialization *)
+assert (Eq:=trans_equal).
+
+specialize Eq.
+specialize Eq with (1:=H)(2:=H0). Undo.
+specialize Eq with (x:=a)(y:=b)(z:=c). Undo.
+specialize Eq with (1:=H)(z:=c). Undo.
+specialize Eq with nat a b c. Undo.
+specialize (Eq nat). Undo.
+specialize (Eq _ a b c). Undo.
+(* no implicit argument for Eq, hence no (Eq (x:=a)) *)
+specialize (Eq _ _ _ _ H H0). Undo.
+specialize (Eq _ _ _ b H0). Undo.
+
+(*
+(** strange behavior to inspect more precisely *)
+
+(* 1) proof aspect : let H:= ... in (fun H => ..) H
+ presque ok... *)
+
+(* 2) echoue moins lorsque zero premise de mangé *)
+specialize trans_equal with (1:=Eq). (* mal typé !! *)
+
+(* 3) *)
+specialize trans_equal with _ a b c. intros _.
+(* Anomaly: Evar ?88 was not declared. Please report. *)
+*)
+
+Abort. \ No newline at end of file
diff --git a/test-suite/success/unification.v b/test-suite/success/unification.v
index 68869621..91ee18ea 100644
--- a/test-suite/success/unification.v
+++ b/test-suite/success/unification.v
@@ -15,6 +15,12 @@ Proof.
intros; apply (H _ H0).
Qed.
+Lemma l3 : (forall P, ~(exists x:nat, P x))
+ -> forall P:nat->Prop, ~(exists x:nat, P x -> P x).
+Proof.
+intros; apply H.
+Qed.
+
(* Example submitted for Zenon *)
@@ -56,10 +62,67 @@ Require Import Arith.
Parameter x y : nat.
Parameter G:x=y->x=y->Prop.
Parameter K:x<>y->x<>y->Prop.
-Lemma l3 : (forall f:x=y->Prop, forall g:x<>y->Prop,
+Lemma l4 : (forall f:x=y->Prop, forall g:x<>y->Prop,
match eq_nat_dec x y with left a => f a | right a => g a end)
-> match eq_nat_dec x y with left a => G a a | right a => K a a end.
Proof.
intros.
apply H.
Qed.
+
+
+(* Test unification modulo eta-expansion (if possible) *)
+
+(* In this example, two instances for ?P (argument of hypothesis H) can be
+ inferred (one is by unifying the type [Q true] and [?P true] of the
+ goal and type of [H]; the other is by unifying the argument of [f]);
+ we need to unify both instances up to allowed eta-expansions of the
+ instances (eta is allowed if the meta was applied to arguments)
+
+ This used to fail before revision 9389 in trunk
+*)
+
+Lemma l5 :
+ forall f : (forall P, P true), (forall P, f P = f P) ->
+ forall Q, f (fun x => Q x) = f (fun x => Q x).
+Proof.
+intros.
+apply H.
+Qed.
+
+(* Test instanciation of evars by unification *)
+
+Goal (forall x, 0 * x = 0 -> True) -> True.
+intros; eapply H.
+rewrite <- plus_n_Sm. (* should refine ?x with S ?x' *)
+Abort.
+
+(* Check handling of identity equation between evars *)
+(* The example failed to pass until revision 10623 *)
+
+Lemma l6 :
+ (forall y, (forall x, (forall z, y = 0 -> y + z = 0) -> y + x = 0) -> True)
+ -> True.
+intros.
+eapply H.
+intros.
+apply H0. (* Check that equation ?n[H] = ?n[H] is correctly considered true *)
+reflexivity.
+Qed.
+
+(* Check treatment of metas erased by K-redexes at the time of turning
+ them to evas *)
+
+Inductive nonemptyT (t : Type) : Prop := nonemptyT_intro : t -> nonemptyT t.
+Goal True.
+try case nonemptyT_intro. (* check that it fails w/o anomaly *)
+Abort.
+
+(* Test handling of return type and when it is decided to make the
+ predicate dependent or not - see "bug" #1851 *)
+
+Goal forall X (a:X) (f':nat -> X), (exists f : nat -> X, True).
+intros.
+exists (fun n => match n with O => a | S n' => f' n' end).
+constructor.
+Qed.
diff --git a/test-suite/success/univers.v b/test-suite/success/univers.v
index 87edc4de..3c2c0883 100644
--- a/test-suite/success/univers.v
+++ b/test-suite/success/univers.v
@@ -56,3 +56,7 @@ intro.
set (C := forall m, Q m -> Q m).
exact I.
Qed.
+
+(* Submitted by Danko Ilik (bug report #1507); related to LetIn *)
+
+Record U : Type := { A:=Type; a:A }.
diff --git a/test-suite/typeclasses/NewSetoid.v b/test-suite/typeclasses/NewSetoid.v
new file mode 100644
index 00000000..8ad03880
--- /dev/null
+++ b/test-suite/typeclasses/NewSetoid.v
@@ -0,0 +1,74 @@
+(************************************************************************)
+(* v * The Coq Proof Assistant / The Coq Development Team *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(************************************************************************)
+
+(* Certified Haskell Prelude.
+ * Author: Matthieu Sozeau
+ * Institution: LRI, CNRS UMR 8623 - UniversitÃcopyright Paris Sud
+ * 91405 Orsay, France *)
+
+(* $Id: FSetAVL_prog.v 616 2007-08-08 12:28:10Z msozeau $ *)
+
+Require Import Coq.Program.Program.
+
+Set Implicit Arguments.
+Unset Strict Implicit.
+
+Require Import Coq.Classes.SetoidTactics.
+
+Goal not True == not (not False) -> ((not True -> True)) \/ True.
+ intros.
+ clrewrite H.
+ clrewrite <- H.
+ right ; auto.
+Defined.
+
+Definition reduced_thm := Eval compute in Unnamed_thm.
+
+(* Print reduced_thm. *)
+
+Lemma foo [ Setoid a R ] : True. (* forall x y, R x y -> x -> y. *)
+Proof.
+ intros.
+ Print respect2.
+ pose setoid_morphism.
+ pose (respect2 (b0:=b)).
+ simpl in b0.
+ unfold binary_respectful in b0.
+ pose (arrow_morphism R).
+ pose (respect2 (b0:=b1)).
+ unfold binary_respectful in b2.
+
+ pose (eq_morphism (A:=a)).
+ pose (respect2 (b0:=b3)).
+ unfold binary_respectful in b4.
+ exact I.
+Qed.
+
+Goal forall A B C (H : A <-> B) (H' : B <-> C), A /\ B <-> B /\ C.
+ intros.
+ Set Printing All.
+ Print iff_morphism.
+ clrewrite H.
+ clrewrite H'.
+ reflexivity.
+Defined.
+
+Goal forall A B C (H : A <-> B) (H' : B <-> C), A /\ B <-> B /\ C.
+ intros.
+ rewrite H.
+ rewrite H'.
+ reflexivity.
+Defined.
+
+Require Import Setoid_tac.
+Require Import Setoid_Prop.
+
+(* Print Unnamed_thm0. *)
+(* Print Unnamed_thm1. *)
+
+
diff --git a/test-suite/typeclasses/clrewrite.v b/test-suite/typeclasses/clrewrite.v
new file mode 100644
index 00000000..2978fda2
--- /dev/null
+++ b/test-suite/typeclasses/clrewrite.v
@@ -0,0 +1,111 @@
+
+Set Implicit Arguments.
+Unset Strict Implicit.
+
+Require Import Coq.Classes.Equivalence.
+
+Section Equiv.
+ Context [ Equivalence A eqA ].
+
+ Variables x y z w : A.
+
+ Goal eqA x y -> eqA y x.
+ intros H ; clrewrite H.
+ refl.
+ Qed.
+
+ Tactic Notation "simpl" "*" := auto || relation_tac.
+
+ Goal eqA x y -> eqA y x /\ True.
+ intros H ; clrewrite H.
+ split ; simpl*.
+ Qed.
+
+ Goal eqA x y -> eqA y x /\ eqA x x.
+ intros H ; clrewrite H.
+ split ; simpl*.
+ Qed.
+
+ Goal eqA x y -> eqA y z -> eqA x y.
+ intros H.
+ clrewrite H.
+ intro. refl.
+ Qed.
+
+ Goal eqA x y -> eqA z y -> eqA x y.
+ intros H.
+ clrewrite <- H at 2.
+ clrewrite <- H at 1.
+ intro. refl.
+ Qed.
+
+ Opaque complement.
+
+ Print iff_inverse_impl_binary_morphism.
+
+ Goal eqA x y -> eqA x y -> eqA x y.
+ intros H.
+ clrewrite H.
+ intro. refl.
+ Qed.
+
+ Goal eqA x y -> eqA x y -> eqA x y.
+ intros H.
+ clrewrite <- H.
+ refl.
+ Qed.
+
+ Goal eqA x y -> True /\ True /\ False /\ eqA x x -> True /\ True /\ False /\ eqA x y.
+ Proof.
+ intros.
+ clrewrite <- H.
+ apply H0.
+ Qed.
+
+End Equiv.
+
+Section Trans.
+ Context [ Transitive A R ].
+
+ Variables x y z w : A.
+
+ Tactic Notation "simpl" "*" := auto || relation_tac.
+
+(* Typeclasses eauto := debug. *)
+
+ Goal R x y -> R y x -> R y y -> R x x.
+ Proof with auto.
+ intros H H' H''.
+
+ clrewrite <- H' at 2.
+ clrewrite H at 1...
+ Qed.
+
+ Goal R x y -> R y z -> R x z.
+ intros H.
+ clrewrite H.
+ refl.
+ Qed.
+
+ Goal R x y -> R z y -> R x y.
+ intros H.
+ clrewrite <- H at 2.
+ intro.
+ clrewrite H at 1.
+ Abort.
+
+ Goal R x y -> True /\ R y z -> True /\ R x z.
+ Proof.
+ intros.
+ clrewrite H.
+ apply H0.
+ Qed.
+
+ Goal R x y -> True /\ True /\ False /\ R y z -> True /\ True /\ False /\ R x z.
+ Proof.
+ intros.
+ clrewrite H.
+ apply H0.
+ Qed.
+
+End Trans.
diff --git a/test-suite/typeclasses/unification_delta.v b/test-suite/typeclasses/unification_delta.v
new file mode 100644
index 00000000..663a837f
--- /dev/null
+++ b/test-suite/typeclasses/unification_delta.v
@@ -0,0 +1,46 @@
+Require Import Coq.Classes.Equivalence.
+Require Import Coq.Program.Program.
+
+Ltac obligations_tactic ::= program_simpl ; simpl_relation.
+
+Lemma bla : forall [ ! Equivalence A (eqA : relation A) ] x y, eqA x y -> eqA y x.
+Proof.
+ intros.
+ rewrite H0.
+ reflexivity.
+Defined.
+
+Lemma bla' : forall [ ! Equivalence A (eqA : relation A) ] x y, eqA x y -> eqA y x.
+Proof.
+ intros.
+ (* Need delta on [relation] to unify with the right lemmas. *)
+ rewrite <- H0.
+ reflexivity.
+Qed.
+
+Axiom euclid : nat -> { x : nat | x > 0 } -> nat.
+
+Definition eq_proj {A} {s : A -> Prop} : relation (sig s) :=
+ fun x y => `x = `y.
+
+Program Instance {A : Type} {s : A -> Prop} => Equivalence (sig s) eq_proj.
+
+ Next Obligation.
+ Proof.
+ constructor ; red ; intros.
+ reflexivity.
+ Qed.
+
+ Admit Obligations.
+
+Instance Morphism (eq ==> eq_proj ==> eq) euclid.
+Proof.
+Admitted.
+
+Goal forall (x : nat) (y : nat | y > 0) (z : nat | z > 0), eq_proj y z -> euclid x y = euclid x z.
+Proof.
+ intros.
+ (* Breaks if too much delta in unification *)
+ rewrite H.
+ reflexivity.
+Qed. \ No newline at end of file