aboutsummaryrefslogtreecommitdiffhomepage
diff options
context:
space:
mode:
authorGravatar Enrico Tassi <Enrico.Tassi@inria.fr>2018-04-12 10:08:05 +0200
committerGravatar Enrico Tassi <Enrico.Tassi@inria.fr>2018-05-15 09:58:47 +0200
commit15059d887c3059e6d925310be860dd2a3cf97796 (patch)
treee0c769cbad3b137e738c3e9da766f7f5f5795428
parent3008ce85ed4de549816a1cac4701cb28bee4fad6 (diff)
[ssr] import ssreflect test suite from math-comp
-rw-r--r--test-suite/Makefile6
-rw-r--r--test-suite/output/ssr_explain_match.out55
-rw-r--r--test-suite/output/ssr_explain_match.v23
-rw-r--r--test-suite/prerequisite/ssr_mini_mathcomp.v1472
-rw-r--r--test-suite/prerequisite/ssr_ssrsyntax1.v36
-rw-r--r--test-suite/ssr/absevarprop.v96
-rw-r--r--test-suite/ssr/abstract_var2.v25
-rw-r--r--test-suite/ssr/binders.v55
-rw-r--r--test-suite/ssr/binders_of.v23
-rw-r--r--test-suite/ssr/caseview.v17
-rw-r--r--test-suite/ssr/congr.v34
-rw-r--r--test-suite/ssr/deferclear.v37
-rw-r--r--test-suite/ssr/dependent_type_err.v20
-rw-r--r--test-suite/ssr/derive_inversion.v29
-rw-r--r--test-suite/ssr/elim.v279
-rw-r--r--test-suite/ssr/elim2.v74
-rw-r--r--test-suite/ssr/elim_pattern.v27
-rw-r--r--test-suite/ssr/first_n.v21
-rw-r--r--test-suite/ssr/gen_have.v174
-rw-r--r--test-suite/ssr/gen_pattern.v33
-rw-r--r--test-suite/ssr/have_TC.v50
-rw-r--r--test-suite/ssr/have_transp.v48
-rw-r--r--test-suite/ssr/have_view_idiom.v18
-rw-r--r--test-suite/ssr/havesuff.v85
-rw-r--r--test-suite/ssr/if_isnt.v22
-rw-r--r--test-suite/ssr/intro_beta.v25
-rw-r--r--test-suite/ssr/intro_noop.v37
-rw-r--r--test-suite/ssr/ipatalternation.v18
-rw-r--r--test-suite/ssr/ltac_have.v39
-rw-r--r--test-suite/ssr/ltac_in.v26
-rw-r--r--test-suite/ssr/move_after.v19
-rw-r--r--test-suite/ssr/multiview.v58
-rw-r--r--test-suite/ssr/occarrow.v23
-rw-r--r--test-suite/ssr/patnoX.v18
-rw-r--r--test-suite/ssr/pattern.v32
-rw-r--r--test-suite/ssr/primproj.v164
-rw-r--r--test-suite/ssr/rewpatterns.v146
-rw-r--r--test-suite/ssr/set_lamda.v27
-rw-r--r--test-suite/ssr/set_pattern.v64
-rw-r--r--test-suite/ssr/ssrsyntax2.v20
-rw-r--r--test-suite/ssr/tc.v39
-rw-r--r--test-suite/ssr/typeof.v22
-rw-r--r--test-suite/ssr/unfold_Opaque.v18
-rw-r--r--test-suite/ssr/unkeyed.v31
-rw-r--r--test-suite/ssr/view_case.v31
-rw-r--r--test-suite/ssr/wlog_suff.v28
-rw-r--r--test-suite/ssr/wlogletin.v50
-rw-r--r--test-suite/ssr/wlong_intro.v20
48 files changed, 3712 insertions, 2 deletions
diff --git a/test-suite/Makefile b/test-suite/Makefile
index 9d84cd5c7..2531b8c67 100644
--- a/test-suite/Makefile
+++ b/test-suite/Makefile
@@ -94,7 +94,7 @@ INTERACTIVE := interactive
VSUBSYSTEMS := prerequisite success failure $(BUGS) output \
output-modulo-time $(INTERACTIVE) micromega $(COMPLEXITY) modules stm \
- coqdoc
+ coqdoc ssr
# All subsystems
SUBSYSTEMS := $(VSUBSYSTEMS) misc bugs ide vio coqchk coqwc coq-makefile
@@ -158,6 +158,7 @@ summary:
$(call summary_dir, "Complexity tests", complexity); \
$(call summary_dir, "Module tests", modules); \
$(call summary_dir, "STM tests", stm); \
+ $(call summary_dir, "SSR tests", ssr); \
$(call summary_dir, "IDE tests", ide); \
$(call summary_dir, "VI tests", vio); \
$(call summary_dir, "Coqchk tests", coqchk); \
@@ -261,7 +262,8 @@ $(addsuffix .log,$(wildcard prerequisite/*.v)): %.v.log: %.v
fi; \
} > "$@"
-$(addsuffix .log,$(wildcard success/*.v micromega/*.v modules/*.v)): %.v.log: %.v $(PREREQUISITELOG)
+ssr: $(wildcard ssr/*.v:%.v=%.v.log)
+$(addsuffix .log,$(wildcard ssr/*.v success/*.v micromega/*.v modules/*.v)): %.v.log: %.v $(PREREQUISITELOG)
@echo "TEST $< $(call get_coq_prog_args_in_parens,"$<")"
$(HIDE){ \
opts="$(if $(findstring modules/,$<),-R modules Mods -impredicative-set)"; \
diff --git a/test-suite/output/ssr_explain_match.out b/test-suite/output/ssr_explain_match.out
new file mode 100644
index 000000000..fa2393b91
--- /dev/null
+++ b/test-suite/output/ssr_explain_match.out
@@ -0,0 +1,55 @@
+File "stdin", line 12, characters 0-61:
+Warning: Notation _ - _ was already used in scope nat_scope.
+[notation-overridden,parsing]
+File "stdin", line 12, characters 0-61:
+Warning: Notation _ <= _ was already used in scope nat_scope.
+[notation-overridden,parsing]
+File "stdin", line 12, characters 0-61:
+Warning: Notation _ < _ was already used in scope nat_scope.
+[notation-overridden,parsing]
+File "stdin", line 12, characters 0-61:
+Warning: Notation _ >= _ was already used in scope nat_scope.
+[notation-overridden,parsing]
+File "stdin", line 12, characters 0-61:
+Warning: Notation _ > _ was already used in scope nat_scope.
+[notation-overridden,parsing]
+File "stdin", line 12, characters 0-61:
+Warning: Notation _ <= _ <= _ was already used in scope nat_scope.
+[notation-overridden,parsing]
+File "stdin", line 12, characters 0-61:
+Warning: Notation _ < _ <= _ was already used in scope nat_scope.
+[notation-overridden,parsing]
+File "stdin", line 12, characters 0-61:
+Warning: Notation _ <= _ < _ was already used in scope nat_scope.
+[notation-overridden,parsing]
+File "stdin", line 12, characters 0-61:
+Warning: Notation _ < _ < _ was already used in scope nat_scope.
+[notation-overridden,parsing]
+File "stdin", line 12, characters 0-61:
+Warning: Notation _ + _ was already used in scope nat_scope.
+[notation-overridden,parsing]
+File "stdin", line 12, characters 0-61:
+Warning: Notation _ * _ was already used in scope nat_scope.
+[notation-overridden,parsing]
+BEGIN INSTANCES
+instance: (x + y + z) matches: (x + y + z)
+instance: (x + y) matches: (x + y)
+instance: (x + y) matches: (x + y)
+END INSTANCES
+BEGIN INSTANCES
+instance: (addnC (x + y) z) matches: (x + y + z)
+instance: (addnC x y) matches: (x + y)
+instance: (addnC x y) matches: (x + y)
+END INSTANCES
+BEGIN INSTANCES
+instance: (addnA x y z) matches: (x + y + z)
+END INSTANCES
+BEGIN INSTANCES
+instance: (addnA x y z) matches: (x + y + z)
+instance: (addnC z (x + y)) matches: (x + y + z)
+instance: (addnC y x) matches: (x + y)
+instance: (addnC y x) matches: (x + y)
+END INSTANCES
+The command has indeed failed with message:
+Ltac call to "ssrinstancesoftpat (cpattern)" failed.
+Not supported
diff --git a/test-suite/output/ssr_explain_match.v b/test-suite/output/ssr_explain_match.v
new file mode 100644
index 000000000..56ca24b6e
--- /dev/null
+++ b/test-suite/output/ssr_explain_match.v
@@ -0,0 +1,23 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+Require Import ssrmatching.
+Require Import ssreflect ssrbool TestSuite.ssr_mini_mathcomp.
+
+Definition addnAC := (addnA, addnC).
+
+Lemma test x y z : x + y + z = x + y.
+
+ssrinstancesoftpat (_ + _).
+ssrinstancesofruleL2R addnC.
+ssrinstancesofruleR2L addnA.
+ssrinstancesofruleR2L addnAC.
+Fail ssrinstancesoftpat (_ + _ in RHS). (* Not implemented *)
+Admitted.
diff --git a/test-suite/prerequisite/ssr_mini_mathcomp.v b/test-suite/prerequisite/ssr_mini_mathcomp.v
new file mode 100644
index 000000000..cb2c56736
--- /dev/null
+++ b/test-suite/prerequisite/ssr_mini_mathcomp.v
@@ -0,0 +1,1472 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* Some code from mathcomp needed in order to run ssr_* tests *)
+
+Require Import ssreflect ssrfun ssrbool.
+
+Global Set SsrOldRewriteGoalsOrder.
+Global Set Asymmetric Patterns.
+Global Set Bullet Behavior "None".
+
+Set Implicit Arguments.
+Unset Strict Implicit.
+Unset Printing Implicit Defensive.
+
+(* eqtype ---------------------------------------------------------- *)
+
+Module Equality.
+
+Definition axiom T (e : rel T) := forall x y, reflect (x = y) (e x y).
+
+Structure mixin_of T := Mixin {op : rel T; _ : axiom op}.
+Notation class_of := mixin_of (only parsing).
+
+Section ClassDef.
+
+Structure type := Pack {sort; _ : class_of sort; _ : Type}.
+Local Coercion sort : type >-> Sortclass.
+Variables (T : Type) (cT : type).
+
+Definition class := let: Pack _ c _ := cT return class_of cT in c.
+
+Definition pack c := @Pack T c T.
+Definition clone := fun c & cT -> T & phant_id (pack c) cT => pack c.
+
+End ClassDef.
+
+Module Exports.
+Coercion sort : type >-> Sortclass.
+Notation eqType := type.
+Notation EqMixin := Mixin.
+Notation EqType T m := (@pack T m).
+Notation "[ 'eqMixin' 'of' T ]" := (class _ : mixin_of T)
+ (at level 0, format "[ 'eqMixin' 'of' T ]") : form_scope.
+Notation "[ 'eqType' 'of' T 'for' C ]" := (@clone T C _ idfun id)
+ (at level 0, format "[ 'eqType' 'of' T 'for' C ]") : form_scope.
+Notation "[ 'eqType' 'of' T ]" := (@clone T _ _ id id)
+ (at level 0, format "[ 'eqType' 'of' T ]") : form_scope.
+End Exports.
+
+End Equality.
+Export Equality.Exports.
+
+Definition eq_op T := Equality.op (Equality.class T).
+
+Lemma eqE T x : eq_op x = Equality.op (Equality.class T) x.
+Proof. by []. Qed.
+
+Lemma eqP T : Equality.axiom (@eq_op T).
+Proof. by case: T => ? []. Qed.
+Arguments eqP [T x y].
+
+Delimit Scope eq_scope with EQ.
+Open Scope eq_scope.
+
+Notation "x == y" := (eq_op x y)
+ (at level 70, no associativity) : bool_scope.
+Notation "x == y :> T" := ((x : T) == (y : T))
+ (at level 70, y at next level) : bool_scope.
+Notation "x != y" := (~~ (x == y))
+ (at level 70, no associativity) : bool_scope.
+Notation "x != y :> T" := (~~ (x == y :> T))
+ (at level 70, y at next level) : bool_scope.
+Notation "x =P y" := (eqP : reflect (x = y) (x == y))
+ (at level 70, no associativity) : eq_scope.
+Notation "x =P y :> T" := (eqP : reflect (x = y :> T) (x == y :> T))
+ (at level 70, y at next level, no associativity) : eq_scope.
+
+Prenex Implicits eq_op eqP.
+
+Lemma eq_refl (T : eqType) (x : T) : x == x. Proof. exact/eqP. Qed.
+Notation eqxx := eq_refl.
+
+Lemma eq_sym (T : eqType) (x y : T) : (x == y) = (y == x).
+Proof. exact/eqP/eqP. Qed.
+
+Hint Resolve eq_refl eq_sym.
+
+
+Definition eqb b := addb (~~ b).
+
+Lemma eqbP : Equality.axiom eqb.
+Proof. by do 2!case; constructor. Qed.
+
+Canonical bool_eqMixin := EqMixin eqbP.
+Canonical bool_eqType := Eval hnf in EqType bool bool_eqMixin.
+
+Section ProdEqType.
+
+Variable T1 T2 : eqType.
+
+Definition pair_eq := [rel u v : T1 * T2 | (u.1 == v.1) && (u.2 == v.2)].
+
+Lemma pair_eqP : Equality.axiom pair_eq.
+Proof.
+move=> [x1 x2] [y1 y2] /=; apply: (iffP andP) => [[]|[<- <-]] //=.
+by do 2!move/eqP->.
+Qed.
+
+Definition prod_eqMixin := EqMixin pair_eqP.
+Canonical prod_eqType := Eval hnf in EqType (T1 * T2) prod_eqMixin.
+
+End ProdEqType.
+
+Section OptionEqType.
+
+Variable T : eqType.
+
+Definition opt_eq (u v : option T) : bool :=
+ oapp (fun x => oapp (eq_op x) false v) (~~ v) u.
+
+Lemma opt_eqP : Equality.axiom opt_eq.
+Proof.
+case=> [x|] [y|] /=; by [constructor | apply: (iffP eqP) => [|[]] ->].
+Qed.
+
+Canonical option_eqMixin := EqMixin opt_eqP.
+Canonical option_eqType := Eval hnf in EqType (option T) option_eqMixin.
+
+End OptionEqType.
+
+Notation xpred1 := (fun a1 x => x == a1).
+Notation xpredU1 := (fun a1 (p : pred _) x => (x == a1) || p x).
+
+Section EqPred.
+
+Variable T : eqType.
+
+Definition pred1 (a1 : T) := SimplPred (xpred1 a1).
+Definition predU1 (a1 : T) p := SimplPred (xpredU1 a1 p).
+
+End EqPred.
+
+Section TransferEqType.
+
+Variables (T : Type) (eT : eqType) (f : T -> eT).
+
+Lemma inj_eqAxiom : injective f -> Equality.axiom (fun x y => f x == f y).
+Proof. by move=> f_inj x y; apply: (iffP eqP) => [|-> //]; apply: f_inj. Qed.
+
+Definition InjEqMixin f_inj := EqMixin (inj_eqAxiom f_inj).
+
+Definition PcanEqMixin g (fK : pcancel f g) := InjEqMixin (pcan_inj fK).
+
+Definition CanEqMixin g (fK : cancel f g) := InjEqMixin (can_inj fK).
+
+End TransferEqType.
+
+(* We use the module system to circumvent a silly limitation that *)
+(* forbids using the same constant to coerce to different targets. *)
+Module Type EqTypePredSig.
+Parameter sort : eqType -> predArgType.
+End EqTypePredSig.
+Module MakeEqTypePred (eqmod : EqTypePredSig).
+Coercion eqmod.sort : eqType >-> predArgType.
+End MakeEqTypePred.
+Module Export EqTypePred := MakeEqTypePred Equality.
+
+
+Section SubType.
+
+Variables (T : Type) (P : pred T).
+
+Structure subType : Type := SubType {
+ sub_sort :> Type;
+ val : sub_sort -> T;
+ Sub : forall x, P x -> sub_sort;
+ _ : forall K (_ : forall x Px, K (@Sub x Px)) u, K u;
+ _ : forall x Px, val (@Sub x Px) = x
+}.
+
+Arguments Sub [s].
+Lemma vrefl : forall x, P x -> x = x. Proof. by []. Qed.
+Definition vrefl_rect := vrefl.
+
+Definition clone_subType U v :=
+ fun sT & sub_sort sT -> U =>
+ fun c Urec cK (sT' := @SubType U v c Urec cK) & phant_id sT' sT => sT'.
+
+Variable sT : subType.
+
+CoInductive Sub_spec : sT -> Type := SubSpec x Px : Sub_spec (Sub x Px).
+
+Lemma SubP u : Sub_spec u.
+Proof. by case: sT Sub_spec SubSpec u => T' _ C rec /= _. Qed.
+
+Lemma SubK x Px : @val sT (Sub x Px) = x.
+Proof. by case: sT. Qed.
+
+Definition insub x :=
+ if @idP (P x) is ReflectT Px then @Some sT (Sub x Px) else None.
+
+Definition insubd u0 x := odflt u0 (insub x).
+
+CoInductive insub_spec x : option sT -> Type :=
+ | InsubSome u of P x & val u = x : insub_spec x (Some u)
+ | InsubNone of ~~ P x : insub_spec x None.
+
+Lemma insubP x : insub_spec x (insub x).
+Proof.
+by rewrite /insub; case: {-}_ / idP; [left; rewrite ?SubK | right; apply/negP].
+Qed.
+
+Lemma insubT x Px : insub x = Some (Sub x Px).
+Admitted.
+
+Lemma insubF x : P x = false -> insub x = None.
+Proof. by move/idP; case: insubP. Qed.
+
+Lemma insubN x : ~~ P x -> insub x = None.
+Proof. by move/negPf/insubF. Qed.
+
+Lemma isSome_insub : ([eta insub] : pred T) =1 P.
+Proof. by apply: fsym => x; case: insubP => // /negPf. Qed.
+
+Lemma insubK : ocancel insub (@val _).
+Proof. by move=> x; case: insubP. Qed.
+
+Lemma valP (u : sT) : P (val u).
+Proof. by case/SubP: u => x Px; rewrite SubK. Qed.
+
+Lemma valK : pcancel (@val _) insub.
+Proof. by case/SubP=> x Px; rewrite SubK; apply: insubT. Qed.
+
+Lemma val_inj : injective (@val sT).
+Proof. exact: pcan_inj valK. Qed.
+
+Lemma valKd u0 : cancel (@val _) (insubd u0).
+Proof. by move=> u; rewrite /insubd valK. Qed.
+
+Lemma val_insubd u0 x : val (insubd u0 x) = if P x then x else val u0.
+Proof. by rewrite /insubd; case: insubP => [u -> | /negPf->]. Qed.
+
+Lemma insubdK u0 : {in P, cancel (insubd u0) (@val _)}.
+Proof. by move=> x Px; rewrite /= val_insubd [P x]Px. Qed.
+
+Definition insub_eq x :=
+ let Some_sub Px := Some (Sub x Px : sT) in
+ let None_sub _ := None in
+ (if P x as Px return P x = Px -> _ then Some_sub else None_sub) (erefl _).
+
+Lemma insub_eqE : insub_eq =1 insub.
+Proof.
+rewrite /insub_eq /insub => x; case: {2 3}_ / idP (erefl _) => // Px Px'.
+by congr (Some _); apply: val_inj; rewrite !SubK.
+Qed.
+
+End SubType.
+
+Arguments SubType [T P].
+Arguments Sub [T P s].
+Arguments vrefl [T P].
+Arguments vrefl_rect [T P].
+Arguments clone_subType [T P] U v [sT] _ [c Urec cK].
+Arguments insub [T P sT].
+Arguments insubT [T] P [sT x].
+Arguments val_inj [T P sT].
+Prenex Implicits val Sub vrefl vrefl_rect insub insubd val_inj.
+
+Local Notation inlined_sub_rect :=
+ (fun K K_S u => let (x, Px) as u return K u := u in K_S x Px).
+
+Local Notation inlined_new_rect :=
+ (fun K K_S u => let (x) as u return K u := u in K_S x).
+
+Notation "[ 'subType' 'for' v ]" := (SubType _ v _ inlined_sub_rect vrefl_rect)
+ (at level 0, only parsing) : form_scope.
+
+Notation "[ 'sub' 'Type' 'for' v ]" := (SubType _ v _ _ vrefl_rect)
+ (at level 0, format "[ 'sub' 'Type' 'for' v ]") : form_scope.
+
+Notation "[ 'subType' 'for' v 'by' rec ]" := (SubType _ v _ rec vrefl)
+ (at level 0, format "[ 'subType' 'for' v 'by' rec ]") : form_scope.
+
+Notation "[ 'subType' 'of' U 'for' v ]" := (clone_subType U v id idfun)
+ (at level 0, format "[ 'subType' 'of' U 'for' v ]") : form_scope.
+
+(*
+Notation "[ 'subType' 'for' v ]" := (clone_subType _ v id idfun)
+ (at level 0, format "[ 'subType' 'for' v ]") : form_scope.
+*)
+Notation "[ 'subType' 'of' U ]" := (clone_subType U _ id id)
+ (at level 0, format "[ 'subType' 'of' U ]") : form_scope.
+
+Definition NewType T U v c Urec :=
+ let Urec' P IH := Urec P (fun x : T => IH x isT : P _) in
+ SubType U v (fun x _ => c x) Urec'.
+Arguments NewType [T U].
+
+Notation "[ 'newType' 'for' v ]" := (NewType v _ inlined_new_rect vrefl_rect)
+ (at level 0, only parsing) : form_scope.
+
+Notation "[ 'new' 'Type' 'for' v ]" := (NewType v _ _ vrefl_rect)
+ (at level 0, format "[ 'new' 'Type' 'for' v ]") : form_scope.
+
+Notation "[ 'newType' 'for' v 'by' rec ]" := (NewType v _ rec vrefl)
+ (at level 0, format "[ 'newType' 'for' v 'by' rec ]") : form_scope.
+
+Definition innew T nT x := @Sub T predT nT x (erefl true).
+Arguments innew [T nT].
+Prenex Implicits innew.
+
+Lemma innew_val T nT : cancel val (@innew T nT).
+Proof. by move=> u; apply: val_inj; apply: SubK. Qed.
+
+(* Prenex Implicits and renaming. *)
+Notation sval := (@proj1_sig _ _).
+Notation "@ 'sval'" := (@proj1_sig) (at level 10, format "@ 'sval'").
+
+Section SubEqType.
+
+Variables (T : eqType) (P : pred T) (sT : subType P).
+
+Local Notation ev_ax := (fun T v => @Equality.axiom T (fun x y => v x == v y)).
+Lemma val_eqP : ev_ax sT val. Proof. exact: inj_eqAxiom val_inj. Qed.
+
+Definition sub_eqMixin := EqMixin val_eqP.
+Canonical sub_eqType := Eval hnf in EqType sT sub_eqMixin.
+
+Definition SubEqMixin :=
+ (let: SubType _ v _ _ _ as sT' := sT
+ return ev_ax sT' val -> Equality.class_of sT' in
+ fun vP : ev_ax _ v => EqMixin vP
+ ) val_eqP.
+
+Lemma val_eqE (u v : sT) : (val u == val v) = (u == v).
+Proof. by []. Qed.
+
+End SubEqType.
+
+Arguments val_eqP [T P sT x y].
+Prenex Implicits val_eqP.
+
+Notation "[ 'eqMixin' 'of' T 'by' <: ]" := (SubEqMixin _ : Equality.class_of T)
+ (at level 0, format "[ 'eqMixin' 'of' T 'by' <: ]") : form_scope.
+
+(* ssrnat ---------------------------------------------------------- *)
+
+Notation succn := Datatypes.S.
+Notation predn := Peano.pred.
+
+Notation "n .+1" := (succn n) (at level 2, left associativity,
+ format "n .+1") : nat_scope.
+Notation "n .+2" := n.+1.+1 (at level 2, left associativity,
+ format "n .+2") : nat_scope.
+Notation "n .+3" := n.+2.+1 (at level 2, left associativity,
+ format "n .+3") : nat_scope.
+Notation "n .+4" := n.+2.+2 (at level 2, left associativity,
+ format "n .+4") : nat_scope.
+
+Notation "n .-1" := (predn n) (at level 2, left associativity,
+ format "n .-1") : nat_scope.
+Notation "n .-2" := n.-1.-1 (at level 2, left associativity,
+ format "n .-2") : nat_scope.
+
+Fixpoint eqn m n {struct m} :=
+ match m, n with
+ | 0, 0 => true
+ | m'.+1, n'.+1 => eqn m' n'
+ | _, _ => false
+ end.
+
+Lemma eqnP : Equality.axiom eqn.
+Proof.
+move=> n m; apply: (iffP idP) => [|<-]; last by elim n.
+by elim: n m => [|n IHn] [|m] //= /IHn->.
+Qed.
+
+Canonical nat_eqMixin := EqMixin eqnP.
+Canonical nat_eqType := Eval hnf in EqType nat nat_eqMixin.
+
+Arguments eqnP [x y].
+Prenex Implicits eqnP.
+
+Coercion nat_of_bool (b : bool) := if b then 1 else 0.
+
+Fixpoint odd n := if n is n'.+1 then ~~ odd n' else false.
+
+Lemma oddb (b : bool) : odd b = b. Proof. by case: b. Qed.
+
+Definition subn_rec := minus.
+Notation "m - n" := (subn_rec m n) : nat_rec_scope.
+
+Definition subn := nosimpl subn_rec.
+Notation "m - n" := (subn m n) : nat_scope.
+
+Definition leq m n := m - n == 0.
+
+Notation "m <= n" := (leq m n) : nat_scope.
+Notation "m < n" := (m.+1 <= n) : nat_scope.
+Notation "m >= n" := (n <= m) (only parsing) : nat_scope.
+Notation "m > n" := (n < m) (only parsing) : nat_scope.
+
+
+Notation "m <= n <= p" := ((m <= n) && (n <= p)) : nat_scope.
+Notation "m < n <= p" := ((m < n) && (n <= p)) : nat_scope.
+Notation "m <= n < p" := ((m <= n) && (n < p)) : nat_scope.
+Notation "m < n < p" := ((m < n) && (n < p)) : nat_scope.
+
+Open Scope nat_scope.
+
+
+Lemma ltnS m n : (m < n.+1) = (m <= n). Proof. by []. Qed.
+Lemma leq0n n : 0 <= n. Proof. by []. Qed.
+Lemma ltn0Sn n : 0 < n.+1. Proof. by []. Qed.
+Lemma ltn0 n : n < 0 = false. Proof. by []. Qed.
+Lemma leqnn n : n <= n. Proof. by elim: n. Qed.
+Hint Resolve leqnn.
+Lemma leqnSn n : n <= n.+1. Proof. by elim: n. Qed.
+
+Lemma leq_trans n m p : m <= n -> n <= p -> m <= p.
+Admitted.
+Lemma leqW m n : m <= n -> m <= n.+1.
+Admitted.
+Hint Resolve leqnSn.
+Lemma ltnW m n : m < n -> m <= n.
+Proof. exact: leq_trans. Qed.
+Hint Resolve ltnW.
+
+Definition addn_rec := plus.
+Notation "m + n" := (addn_rec m n) : nat_rec_scope.
+
+Definition addn := nosimpl addn_rec.
+Notation "m + n" := (addn m n) : nat_scope.
+
+Lemma addn0 : right_id 0 addn. Proof. by move=> n; apply/eqP; elim: n. Qed.
+Lemma add0n : left_id 0 addn. Proof. by []. Qed.
+Lemma addSn m n : m.+1 + n = (m + n).+1. Proof. by []. Qed.
+Lemma addnS m n : m + n.+1 = (m + n).+1. Proof. by elim: m. Qed.
+
+Lemma addnCA : left_commutative addn.
+Proof. by move=> m n p; elim: m => //= m; rewrite addnS => <-. Qed.
+
+Lemma addnC : commutative addn.
+Proof. by move=> m n; rewrite -{1}[n]addn0 addnCA addn0. Qed.
+
+Lemma addnA : associative addn.
+Proof. by move=> m n p; rewrite (addnC n) addnCA addnC. Qed.
+
+Lemma subnK m n : m <= n -> (n - m) + m = n.
+Admitted.
+
+
+Definition muln_rec := mult.
+Notation "m * n" := (muln_rec m n) : nat_rec_scope.
+
+Definition muln := nosimpl muln_rec.
+Notation "m * n" := (muln m n) : nat_scope.
+
+Lemma mul0n : left_zero 0 muln. Proof. by []. Qed.
+Lemma muln0 : right_zero 0 muln. Proof. by elim. Qed.
+Lemma mul1n : left_id 1 muln. Proof. exact: addn0. Qed.
+
+Lemma mulSn m n : m.+1 * n = n + m * n. Proof. by []. Qed.
+Lemma mulSnr m n : m.+1 * n = m * n + n. Proof. exact: addnC. Qed.
+
+Lemma mulnS m n : m * n.+1 = m + m * n.
+Proof. by elim: m => // m; rewrite !mulSn !addSn addnCA => ->. Qed.
+
+Lemma mulnSr m n : m * n.+1 = m * n + m.
+Proof. by rewrite addnC mulnS. Qed.
+
+Lemma muln1 : right_id 1 muln.
+Proof. by move=> n; rewrite mulnSr muln0. Qed.
+
+Lemma mulnC : commutative muln.
+Proof.
+by move=> m n; elim: m => [|m]; rewrite (muln0, mulnS) // mulSn => ->.
+Qed.
+
+Lemma mulnDl : left_distributive muln addn.
+Proof. by move=> m1 m2 n; elim: m1 => //= m1 IHm; rewrite -addnA -IHm. Qed.
+
+Lemma mulnDr : right_distributive muln addn.
+Proof. by move=> m n1 n2; rewrite !(mulnC m) mulnDl. Qed.
+
+Lemma mulnA : associative muln.
+Proof. by move=> m n p; elim: m => //= m; rewrite mulSn mulnDl => ->. Qed.
+
+Lemma mulnCA : left_commutative muln.
+Proof. by move=> m n1 n2; rewrite !mulnA (mulnC m). Qed.
+
+Lemma mulnAC : right_commutative muln.
+Proof. by move=> m n p; rewrite -!mulnA (mulnC n). Qed.
+
+Lemma mulnACA : interchange muln muln.
+Proof. by move=> m n p q; rewrite -!mulnA (mulnCA n). Qed.
+
+(* seq ------------------------------------------------------------- *)
+
+Delimit Scope seq_scope with SEQ.
+Open Scope seq_scope.
+
+(* Inductive seq (T : Type) : Type := Nil | Cons of T & seq T. *)
+Notation seq := list.
+Prenex Implicits cons.
+Notation Cons T := (@cons T) (only parsing).
+Notation Nil T := (@nil T) (only parsing).
+
+Bind Scope seq_scope with list.
+Arguments cons _%type _ _%SEQ.
+
+(* As :: and ++ are (improperly) declared in Init.datatypes, we only rebind *)
+(* them here. *)
+Infix "::" := cons : seq_scope.
+
+(* GG - this triggers a camlp4 warning, as if this Notation had been Reserved *)
+Notation "[ :: ]" := nil (at level 0, format "[ :: ]") : seq_scope.
+
+Notation "[ :: x1 ]" := (x1 :: [::])
+ (at level 0, format "[ :: x1 ]") : seq_scope.
+
+Notation "[ :: x & s ]" := (x :: s) (at level 0, only parsing) : seq_scope.
+
+Notation "[ :: x1 , x2 , .. , xn & s ]" := (x1 :: x2 :: .. (xn :: s) ..)
+ (at level 0, format
+ "'[hv' [ :: '[' x1 , '/' x2 , '/' .. , '/' xn ']' '/ ' & s ] ']'"
+ ) : seq_scope.
+
+Notation "[ :: x1 ; x2 ; .. ; xn ]" := (x1 :: x2 :: .. [:: xn] ..)
+ (at level 0, format "[ :: '[' x1 ; '/' x2 ; '/' .. ; '/' xn ']' ]"
+ ) : seq_scope.
+
+Section Sequences.
+
+Variable n0 : nat. (* numerical parameter for take, drop et al *)
+Variable T : Type. (* must come before the implicit Type *)
+Variable x0 : T. (* default for head/nth *)
+
+Implicit Types x y z : T.
+Implicit Types m n : nat.
+Implicit Type s : seq T.
+
+Fixpoint size s := if s is _ :: s' then (size s').+1 else 0.
+
+Fixpoint cat s1 s2 := if s1 is x :: s1' then x :: s1' ++ s2 else s2
+where "s1 ++ s2" := (cat s1 s2) : seq_scope.
+
+Lemma cat0s s : [::] ++ s = s. Proof. by []. Qed.
+
+Lemma cats0 s : s ++ [::] = s.
+Proof. by elim: s => //= x s ->. Qed.
+
+Lemma catA s1 s2 s3 : s1 ++ s2 ++ s3 = (s1 ++ s2) ++ s3.
+Proof. by elim: s1 => //= x s1 ->. Qed.
+
+Fixpoint nth s n {struct n} :=
+ if s is x :: s' then if n is n'.+1 then @nth s' n' else x else x0.
+
+Fixpoint rcons s z := if s is x :: s' then x :: rcons s' z else [:: z].
+
+CoInductive last_spec : seq T -> Type :=
+ | LastNil : last_spec [::]
+ | LastRcons s x : last_spec (rcons s x).
+
+Lemma lastP s : last_spec s.
+Proof using. Admitted.
+
+Lemma last_ind P :
+ P [::] -> (forall s x, P s -> P (rcons s x)) -> forall s, P s.
+Proof using. Admitted.
+
+
+Section Map.
+
+Variables (T2 : Type) (f : T -> T2).
+
+Fixpoint map s := if s is x :: s' then f x :: map s' else [::].
+
+End Map.
+
+Section SeqFind.
+
+Variable a : pred T.
+
+Fixpoint count s := if s is x :: s' then a x + count s' else 0.
+
+Fixpoint filter s :=
+ if s is x :: s' then if a x then x :: filter s' else filter s' else [::].
+
+End SeqFind.
+
+End Sequences.
+
+Infix "++" := cat : seq_scope.
+
+Notation count_mem x := (count (pred_of_simpl (pred1 x))).
+
+Section EqSeq.
+
+Variables (n0 : nat) (T : eqType) (x0 : T).
+Local Notation nth := (nth x0).
+Implicit Type s : seq T.
+Implicit Types x y z : T.
+
+Fixpoint eqseq s1 s2 {struct s2} :=
+ match s1, s2 with
+ | [::], [::] => true
+ | x1 :: s1', x2 :: s2' => (x1 == x2) && eqseq s1' s2'
+ | _, _ => false
+ end.
+
+Lemma eqseqP : Equality.axiom eqseq.
+Proof.
+move; elim=> [|x1 s1 IHs] [|x2 s2]; do [by constructor | simpl].
+case: (x1 =P x2) => [<-|neqx]; last by right; case.
+by apply: (iffP (IHs s2)) => [<-|[]].
+Qed.
+
+Canonical seq_eqMixin := EqMixin eqseqP.
+Canonical seq_eqType := Eval hnf in EqType (seq T) seq_eqMixin.
+
+Fixpoint mem_seq (s : seq T) :=
+ if s is y :: s' then xpredU1 y (mem_seq s') else xpred0.
+
+Definition eqseq_class := seq T.
+Identity Coercion seq_of_eqseq : eqseq_class >-> seq.
+Coercion pred_of_eq_seq (s : eqseq_class) : pred_class := [eta mem_seq s].
+
+Canonical seq_predType := @mkPredType T (seq T) pred_of_eq_seq.
+
+Fixpoint uniq s := if s is x :: s' then (x \notin s') && uniq s' else true.
+
+End EqSeq.
+
+Definition bitseq := seq bool.
+Canonical bitseq_eqType := Eval hnf in [eqType of bitseq].
+Canonical bitseq_predType := Eval hnf in [predType of bitseq].
+
+Section Pmap.
+
+Variables (aT rT : Type) (f : aT -> option rT) (g : rT -> aT).
+
+Fixpoint pmap s :=
+ if s is x :: s' then let r := pmap s' in oapp (cons^~ r) r (f x) else [::].
+
+End Pmap.
+
+Fixpoint iota m n := if n is n'.+1 then m :: iota m.+1 n' else [::].
+
+Section FoldRight.
+
+Variables (T : Type) (R : Type) (f : T -> R -> R) (z0 : R).
+
+Fixpoint foldr s := if s is x :: s' then f x (foldr s') else z0.
+
+End FoldRight.
+
+Lemma mem_iota m n i : (i \in iota m n) = (m <= i) && (i < m + n).
+Admitted.
+
+
+(* choice ------------------------------------------------------------- *)
+
+Module Choice.
+
+Section ClassDef.
+
+Record mixin_of T := Mixin {
+ find : pred T -> nat -> option T;
+ _ : forall P n x, find P n = Some x -> P x;
+ _ : forall P : pred T, (exists x, P x) -> exists n, find P n;
+ _ : forall P Q : pred T, P =1 Q -> find P =1 find Q
+}.
+
+Record class_of T := Class {base : Equality.class_of T; mixin : mixin_of T}.
+Local Coercion base : class_of >-> Equality.class_of.
+
+Structure type := Pack {sort; _ : class_of sort; _ : Type}.
+Local Coercion sort : type >-> Sortclass.
+Variables (T : Type) (cT : type).
+Definition class := let: Pack _ c _ as cT' := cT return class_of cT' in c.
+Definition clone c of phant_id class c := @Pack T c T.
+Let xT := let: Pack T _ _ := cT in T.
+Notation xclass := (class : class_of xT).
+
+Definition pack m :=
+ fun b bT & phant_id (Equality.class bT) b => Pack (@Class T b m) T.
+
+(* Inheritance *)
+Definition eqType := @Equality.Pack cT xclass xT.
+
+End ClassDef.
+
+Module Import Exports.
+Coercion base : class_of >-> Equality.class_of.
+Coercion sort : type >-> Sortclass.
+Coercion eqType : type >-> Equality.type.
+Canonical eqType.
+Notation choiceType := type.
+Notation choiceMixin := mixin_of.
+Notation ChoiceType T m := (@pack T m _ _ id).
+Notation "[ 'choiceType' 'of' T 'for' cT ]" := (@clone T cT _ idfun)
+ (at level 0, format "[ 'choiceType' 'of' T 'for' cT ]") : form_scope.
+Notation "[ 'choiceType' 'of' T ]" := (@clone T _ _ id)
+ (at level 0, format "[ 'choiceType' 'of' T ]") : form_scope.
+
+End Exports.
+
+End Choice.
+Export Choice.Exports.
+
+Section ChoiceTheory.
+
+Variable T : choiceType.
+
+Section CanChoice.
+
+Variables (sT : Type) (f : sT -> T).
+
+Lemma PcanChoiceMixin f' : pcancel f f' -> choiceMixin sT.
+Admitted.
+
+Definition CanChoiceMixin f' (fK : cancel f f') :=
+ PcanChoiceMixin (can_pcan fK).
+
+End CanChoice.
+
+Section SubChoice.
+
+Variables (P : pred T) (sT : subType P).
+
+Definition sub_choiceMixin := PcanChoiceMixin (@valK T P sT).
+Definition sub_choiceClass := @Choice.Class sT (sub_eqMixin sT) sub_choiceMixin.
+Canonical sub_choiceType := Choice.Pack sub_choiceClass sT.
+
+End SubChoice.
+
+
+Fact seq_choiceMixin : choiceMixin (seq T).
+Admitted.
+Canonical seq_choiceType := Eval hnf in ChoiceType (seq T) seq_choiceMixin.
+End ChoiceTheory.
+
+Fact nat_choiceMixin : choiceMixin nat.
+Proof.
+pose f := [fun (P : pred nat) n => if P n then Some n else None].
+exists f => [P n m | P [n Pn] | P Q eqPQ n] /=; last by rewrite eqPQ.
+ by case: ifP => // Pn [<-].
+by exists n; rewrite Pn.
+Qed.
+Canonical nat_choiceType := Eval hnf in ChoiceType nat nat_choiceMixin.
+
+Definition bool_choiceMixin := CanChoiceMixin oddb.
+Canonical bool_choiceType := Eval hnf in ChoiceType bool bool_choiceMixin.
+Canonical bitseq_choiceType := Eval hnf in [choiceType of bitseq].
+
+
+Notation "[ 'choiceMixin' 'of' T 'by' <: ]" :=
+ (sub_choiceMixin _ : choiceMixin T)
+ (at level 0, format "[ 'choiceMixin' 'of' T 'by' <: ]") : form_scope.
+
+
+
+
+Module Countable.
+
+Record mixin_of (T : Type) : Type := Mixin {
+ pickle : T -> nat;
+ unpickle : nat -> option T;
+ pickleK : pcancel pickle unpickle
+}.
+
+Definition EqMixin T m := PcanEqMixin (@pickleK T m).
+Definition ChoiceMixin T m := PcanChoiceMixin (@pickleK T m).
+
+Section ClassDef.
+
+Record class_of T := Class { base : Choice.class_of T; mixin : mixin_of T }.
+Local Coercion base : class_of >-> Choice.class_of.
+
+Structure type : Type := Pack {sort : Type; _ : class_of sort; _ : Type}.
+Local Coercion sort : type >-> Sortclass.
+Variables (T : Type) (cT : type).
+Definition class := let: Pack _ c _ as cT' := cT return class_of cT' in c.
+Definition clone c of phant_id class c := @Pack T c T.
+Let xT := let: Pack T _ _ := cT in T.
+Notation xclass := (class : class_of xT).
+
+Definition pack m :=
+ fun bT b & phant_id (Choice.class bT) b => Pack (@Class T b m) T.
+
+Definition eqType := @Equality.Pack cT xclass xT.
+Definition choiceType := @Choice.Pack cT xclass xT.
+
+End ClassDef.
+
+Module Exports.
+Coercion base : class_of >-> Choice.class_of.
+Coercion mixin : class_of >-> mixin_of.
+Coercion sort : type >-> Sortclass.
+Coercion eqType : type >-> Equality.type.
+Canonical eqType.
+Coercion choiceType : type >-> Choice.type.
+Canonical choiceType.
+Notation countType := type.
+Notation CountType T m := (@pack T m _ _ id).
+Notation CountMixin := Mixin.
+Notation CountChoiceMixin := ChoiceMixin.
+Notation "[ 'countType' 'of' T 'for' cT ]" := (@clone T cT _ idfun)
+ (at level 0, format "[ 'countType' 'of' T 'for' cT ]") : form_scope.
+Notation "[ 'countType' 'of' T ]" := (@clone T _ _ id)
+ (at level 0, format "[ 'countType' 'of' T ]") : form_scope.
+
+End Exports.
+
+End Countable.
+Export Countable.Exports.
+
+Definition unpickle T := Countable.unpickle (Countable.class T).
+Definition pickle T := Countable.pickle (Countable.class T).
+Arguments unpickle [T].
+Prenex Implicits pickle unpickle.
+
+Section CountableTheory.
+
+Variable T : countType.
+
+Lemma pickleK : @pcancel nat T pickle unpickle.
+Proof. exact: Countable.pickleK. Qed.
+
+Definition pickle_inv n :=
+ obind (fun x : T => if pickle x == n then Some x else None) (unpickle n).
+
+Lemma pickle_invK : ocancel pickle_inv pickle.
+Proof.
+by rewrite /pickle_inv => n; case def_x: (unpickle n) => //= [x]; case: eqP.
+Qed.
+
+Lemma pickleK_inv : pcancel pickle pickle_inv.
+Proof. by rewrite /pickle_inv => x; rewrite pickleK /= eqxx. Qed.
+
+Lemma pcan_pickleK sT f f' :
+ @pcancel T sT f f' -> pcancel (pickle \o f) (pcomp f' unpickle).
+Proof. by move=> fK x; rewrite /pcomp pickleK /= fK. Qed.
+
+Definition PcanCountMixin sT f f' (fK : pcancel f f') :=
+ @CountMixin sT _ _ (pcan_pickleK fK).
+
+Definition CanCountMixin sT f f' (fK : cancel f f') :=
+ @PcanCountMixin sT _ _ (can_pcan fK).
+
+Definition sub_countMixin P sT := PcanCountMixin (@valK T P sT).
+
+End CountableTheory.
+Notation "[ 'countMixin' 'of' T 'by' <: ]" :=
+ (sub_countMixin _ : Countable.mixin_of T)
+ (at level 0, format "[ 'countMixin' 'of' T 'by' <: ]") : form_scope.
+
+Section SubCountType.
+
+Variables (T : choiceType) (P : pred T).
+Import Countable.
+
+Structure subCountType : Type :=
+ SubCountType {subCount_sort :> subType P; _ : mixin_of subCount_sort}.
+
+Coercion sub_countType (sT : subCountType) :=
+ Eval hnf in pack (let: SubCountType _ m := sT return mixin_of sT in m) id.
+Canonical sub_countType.
+
+Definition pack_subCountType U :=
+ fun sT cT & sub_sort sT * sort cT -> U * U =>
+ fun b m & phant_id (Class b m) (class cT) => @SubCountType sT m.
+
+End SubCountType.
+
+(* This assumes that T has both countType and subType structures. *)
+Notation "[ 'subCountType' 'of' T ]" :=
+ (@pack_subCountType _ _ T _ _ id _ _ id)
+ (at level 0, format "[ 'subCountType' 'of' T ]") : form_scope.
+
+Lemma nat_pickleK : pcancel id (@Some nat). Proof. by []. Qed.
+Definition nat_countMixin := CountMixin nat_pickleK.
+Canonical nat_countType := Eval hnf in CountType nat nat_countMixin.
+
+(* fintype --------------------------------------------------------- *)
+
+Module Finite.
+
+Section RawMixin.
+
+Variable T : eqType.
+
+Definition axiom e := forall x : T, count_mem x e = 1.
+
+Lemma uniq_enumP e : uniq e -> e =i T -> axiom e.
+Admitted.
+
+Record mixin_of := Mixin {
+ mixin_base : Countable.mixin_of T;
+ mixin_enum : seq T;
+ _ : axiom mixin_enum
+}.
+
+End RawMixin.
+
+Section Mixins.
+
+Variable T : countType.
+
+Definition EnumMixin :=
+ let: Countable.Pack _ (Countable.Class _ m) _ as cT := T
+ return forall e : seq cT, axiom e -> mixin_of cT in
+ @Mixin (EqType _ _) m.
+
+Definition UniqMixin e Ue eT := @EnumMixin e (uniq_enumP Ue eT).
+
+Variable n : nat.
+
+End Mixins.
+
+Section ClassDef.
+
+Record class_of T := Class {
+ base : Choice.class_of T;
+ mixin : mixin_of (Equality.Pack base T)
+}.
+Definition base2 T c := Countable.Class (@base T c) (mixin_base (mixin c)).
+Local Coercion base : class_of >-> Choice.class_of.
+
+Structure type : Type := Pack {sort; _ : class_of sort; _ : Type}.
+Local Coercion sort : type >-> Sortclass.
+Variables (T : Type) (cT : type).
+Definition class := let: Pack _ c _ as cT' := cT return class_of cT' in c.
+Definition clone c of phant_id class c := @Pack T c T.
+Let xT := let: Pack T _ _ := cT in T.
+Notation xclass := (class : class_of xT).
+
+Definition pack b0 (m0 : mixin_of (EqType T b0)) :=
+ fun bT b & phant_id (Choice.class bT) b =>
+ fun m & phant_id m0 m => Pack (@Class T b m) T.
+
+Definition eqType := @Equality.Pack cT xclass xT.
+Definition choiceType := @Choice.Pack cT xclass xT.
+Definition countType := @Countable.Pack cT (base2 xclass) xT.
+
+End ClassDef.
+
+Module Import Exports.
+Coercion mixin_base : mixin_of >-> Countable.mixin_of.
+Coercion base : class_of >-> Choice.class_of.
+Coercion mixin : class_of >-> mixin_of.
+Coercion base2 : class_of >-> Countable.class_of.
+Coercion sort : type >-> Sortclass.
+Coercion eqType : type >-> Equality.type.
+Canonical eqType.
+Coercion choiceType : type >-> Choice.type.
+Canonical choiceType.
+Coercion countType : type >-> Countable.type.
+Canonical countType.
+Notation finType := type.
+Notation FinType T m := (@pack T _ m _ _ id _ id).
+Notation FinMixin := EnumMixin.
+Notation UniqFinMixin := UniqMixin.
+Notation "[ 'finType' 'of' T 'for' cT ]" := (@clone T cT _ idfun)
+ (at level 0, format "[ 'finType' 'of' T 'for' cT ]") : form_scope.
+Notation "[ 'finType' 'of' T ]" := (@clone T _ _ id)
+ (at level 0, format "[ 'finType' 'of' T ]") : form_scope.
+End Exports.
+
+Module Type EnumSig.
+Parameter enum : forall cT : type, seq cT.
+Axiom enumDef : enum = fun cT => mixin_enum (class cT).
+End EnumSig.
+
+Module EnumDef : EnumSig.
+Definition enum cT := mixin_enum (class cT).
+Definition enumDef := erefl enum.
+End EnumDef.
+
+Notation enum := EnumDef.enum.
+
+End Finite.
+Export Finite.Exports.
+
+Section SubFinType.
+
+Variables (T : choiceType) (P : pred T).
+Import Finite.
+
+Structure subFinType := SubFinType {
+ subFin_sort :> subType P;
+ _ : mixin_of (sub_eqType subFin_sort)
+}.
+
+Definition pack_subFinType U :=
+ fun cT b m & phant_id (class cT) (@Class U b m) =>
+ fun sT m' & phant_id m' m => @SubFinType sT m'.
+
+Implicit Type sT : subFinType.
+
+Definition subFin_mixin sT :=
+ let: SubFinType _ m := sT return mixin_of (sub_eqType sT) in m.
+
+Coercion subFinType_subCountType sT := @SubCountType _ _ sT (subFin_mixin sT).
+Canonical subFinType_subCountType.
+
+Coercion subFinType_finType sT :=
+ Pack (@Class sT (sub_choiceClass sT) (subFin_mixin sT)) sT.
+Canonical subFinType_finType.
+
+Definition enum_mem T (mA : mem_pred _) := filter mA (Finite.enum T).
+Definition image_mem T T' f mA : seq T' := map f (@enum_mem T mA).
+Definition codom T T' f := @image_mem T T' f (mem T).
+
+Lemma codom_val sT x : (x \in codom (val : sT -> T)) = P x.
+Admitted.
+
+End SubFinType.
+
+
+(* This assumes that T has both finType and subCountType structures. *)
+Notation "[ 'subFinType' 'of' T ]" := (@pack_subFinType _ _ T _ _ _ id _ _ id)
+ (at level 0, format "[ 'subFinType' 'of' T ]") : form_scope.
+
+
+
+Section OrdinalSub.
+
+Variable n : nat.
+
+Inductive ordinal : predArgType := Ordinal m of m < n.
+
+Coercion nat_of_ord i := let: Ordinal m _ := i in m.
+
+Canonical ordinal_subType := [subType for nat_of_ord].
+Definition ordinal_eqMixin := Eval hnf in [eqMixin of ordinal by <:].
+Canonical ordinal_eqType := Eval hnf in EqType ordinal ordinal_eqMixin.
+Definition ordinal_choiceMixin := [choiceMixin of ordinal by <:].
+Canonical ordinal_choiceType :=
+ Eval hnf in ChoiceType ordinal ordinal_choiceMixin.
+Definition ordinal_countMixin := [countMixin of ordinal by <:].
+Canonical ordinal_countType := Eval hnf in CountType ordinal ordinal_countMixin.
+Canonical ordinal_subCountType := [subCountType of ordinal].
+
+Lemma ltn_ord (i : ordinal) : i < n. Proof. exact: valP i. Qed.
+
+Lemma ord_inj : injective nat_of_ord. Proof. exact: val_inj. Qed.
+
+Definition ord_enum : seq ordinal := pmap insub (iota 0 n).
+
+Lemma val_ord_enum : map val ord_enum = iota 0 n.
+Admitted.
+
+Lemma ord_enum_uniq : uniq ord_enum.
+Admitted.
+
+Lemma mem_ord_enum i : i \in ord_enum.
+Admitted.
+
+Definition ordinal_finMixin :=
+ Eval hnf in UniqFinMixin ord_enum_uniq mem_ord_enum.
+Canonical ordinal_finType := Eval hnf in FinType ordinal ordinal_finMixin.
+Canonical ordinal_subFinType := Eval hnf in [subFinType of ordinal].
+
+End OrdinalSub.
+
+Notation "''I_' n" := (ordinal n)
+ (at level 8, n at level 2, format "''I_' n").
+
+(* bigop ----------------------------------------------------------------- *)
+
+Reserved Notation "\big [ op / idx ]_ i F"
+ (at level 36, F at level 36, op, idx at level 10, i at level 0,
+ right associativity,
+ format "'[' \big [ op / idx ]_ i '/ ' F ']'").
+Reserved Notation "\big [ op / idx ]_ ( i <- r | P ) F"
+ (at level 36, F at level 36, op, idx at level 10, i, r at level 50,
+ format "'[' \big [ op / idx ]_ ( i <- r | P ) '/ ' F ']'").
+Reserved Notation "\big [ op / idx ]_ ( i <- r ) F"
+ (at level 36, F at level 36, op, idx at level 10, i, r at level 50,
+ format "'[' \big [ op / idx ]_ ( i <- r ) '/ ' F ']'").
+Reserved Notation "\big [ op / idx ]_ ( m <= i < n | P ) F"
+ (at level 36, F at level 36, op, idx at level 10, m, i, n at level 50,
+ format "'[' \big [ op / idx ]_ ( m <= i < n | P ) F ']'").
+Reserved Notation "\big [ op / idx ]_ ( m <= i < n ) F"
+ (at level 36, F at level 36, op, idx at level 10, i, m, n at level 50,
+ format "'[' \big [ op / idx ]_ ( m <= i < n ) '/ ' F ']'").
+Reserved Notation "\big [ op / idx ]_ ( i | P ) F"
+ (at level 36, F at level 36, op, idx at level 10, i at level 50,
+ format "'[' \big [ op / idx ]_ ( i | P ) '/ ' F ']'").
+Reserved Notation "\big [ op / idx ]_ ( i : t | P ) F"
+ (at level 36, F at level 36, op, idx at level 10, i at level 50,
+ format "'[' \big [ op / idx ]_ ( i : t | P ) '/ ' F ']'").
+Reserved Notation "\big [ op / idx ]_ ( i : t ) F"
+ (at level 36, F at level 36, op, idx at level 10, i at level 50,
+ format "'[' \big [ op / idx ]_ ( i : t ) '/ ' F ']'").
+Reserved Notation "\big [ op / idx ]_ ( i < n | P ) F"
+ (at level 36, F at level 36, op, idx at level 10, i, n at level 50,
+ format "'[' \big [ op / idx ]_ ( i < n | P ) '/ ' F ']'").
+Reserved Notation "\big [ op / idx ]_ ( i < n ) F"
+ (at level 36, F at level 36, op, idx at level 10, i, n at level 50,
+ format "'[' \big [ op / idx ]_ ( i < n ) F ']'").
+Reserved Notation "\big [ op / idx ]_ ( i 'in' A | P ) F"
+ (at level 36, F at level 36, op, idx at level 10, i, A at level 50,
+ format "'[' \big [ op / idx ]_ ( i 'in' A | P ) '/ ' F ']'").
+Reserved Notation "\big [ op / idx ]_ ( i 'in' A ) F"
+ (at level 36, F at level 36, op, idx at level 10, i, A at level 50,
+ format "'[' \big [ op / idx ]_ ( i 'in' A ) '/ ' F ']'").
+
+Module Monoid.
+
+Section Definitions.
+Variables (T : Type) (idm : T).
+
+Structure law := Law {
+ operator : T -> T -> T;
+ _ : associative operator;
+ _ : left_id idm operator;
+ _ : right_id idm operator
+}.
+Local Coercion operator : law >-> Funclass.
+
+Structure com_law := ComLaw {
+ com_operator : law;
+ _ : commutative com_operator
+}.
+Local Coercion com_operator : com_law >-> law.
+
+Structure mul_law := MulLaw {
+ mul_operator : T -> T -> T;
+ _ : left_zero idm mul_operator;
+ _ : right_zero idm mul_operator
+}.
+Local Coercion mul_operator : mul_law >-> Funclass.
+
+Structure add_law (mul : T -> T -> T) := AddLaw {
+ add_operator : com_law;
+ _ : left_distributive mul add_operator;
+ _ : right_distributive mul add_operator
+}.
+Local Coercion add_operator : add_law >-> com_law.
+
+Let op_id (op1 op2 : T -> T -> T) := phant_id op1 op2.
+
+Definition clone_law op :=
+ fun (opL : law) & op_id opL op =>
+ fun opmA op1m opm1 (opL' := @Law op opmA op1m opm1)
+ & phant_id opL' opL => opL'.
+
+Definition clone_com_law op :=
+ fun (opL : law) (opC : com_law) & op_id opL op & op_id opC op =>
+ fun opmC (opC' := @ComLaw opL opmC) & phant_id opC' opC => opC'.
+
+Definition clone_mul_law op :=
+ fun (opM : mul_law) & op_id opM op =>
+ fun op0m opm0 (opM' := @MulLaw op op0m opm0) & phant_id opM' opM => opM'.
+
+Definition clone_add_law mop aop :=
+ fun (opC : com_law) (opA : add_law mop) & op_id opC aop & op_id opA aop =>
+ fun mopDm mopmD (opA' := @AddLaw mop opC mopDm mopmD)
+ & phant_id opA' opA => opA'.
+
+End Definitions.
+
+Module Import Exports.
+Coercion operator : law >-> Funclass.
+Coercion com_operator : com_law >-> law.
+Coercion mul_operator : mul_law >-> Funclass.
+Coercion add_operator : add_law >-> com_law.
+Notation "[ 'law' 'of' f ]" := (@clone_law _ _ f _ id _ _ _ id)
+ (at level 0, format"[ 'law' 'of' f ]") : form_scope.
+Notation "[ 'com_law' 'of' f ]" := (@clone_com_law _ _ f _ _ id id _ id)
+ (at level 0, format "[ 'com_law' 'of' f ]") : form_scope.
+Notation "[ 'mul_law' 'of' f ]" := (@clone_mul_law _ _ f _ id _ _ id)
+ (at level 0, format"[ 'mul_law' 'of' f ]") : form_scope.
+Notation "[ 'add_law' m 'of' a ]" := (@clone_add_law _ _ m a _ _ id id _ _ id)
+ (at level 0, format "[ 'add_law' m 'of' a ]") : form_scope.
+End Exports.
+
+Section CommutativeAxioms.
+
+Variable (T : Type) (zero one : T) (mul add : T -> T -> T) (inv : T -> T).
+Hypothesis mulC : commutative mul.
+
+Lemma mulC_id : left_id one mul -> right_id one mul.
+Proof. by move=> mul1x x; rewrite mulC. Qed.
+
+Lemma mulC_zero : left_zero zero mul -> right_zero zero mul.
+Proof. by move=> mul0x x; rewrite mulC. Qed.
+
+Lemma mulC_dist : left_distributive mul add -> right_distributive mul add.
+Proof. by move=> mul_addl x y z; rewrite !(mulC x). Qed.
+
+End CommutativeAxioms.
+Module Theory.
+
+Section Theory.
+Variables (T : Type) (idm : T).
+
+Section Plain.
+Variable mul : law idm.
+Lemma mul1m : left_id idm mul. Proof. by case mul. Qed.
+Lemma mulm1 : right_id idm mul. Proof. by case mul. Qed.
+Lemma mulmA : associative mul. Proof. by case mul. Qed.
+(*Lemma iteropE n x : iterop n mul x idm = iter n (mul x) idm.*)
+
+End Plain.
+
+Section Commutative.
+Variable mul : com_law idm.
+Lemma mulmC : commutative mul. Proof. by case mul. Qed.
+Lemma mulmCA : left_commutative mul.
+Proof. by move=> x y z; rewrite !mulmA (mulmC x). Qed.
+Lemma mulmAC : right_commutative mul.
+Proof. by move=> x y z; rewrite -!mulmA (mulmC y). Qed.
+Lemma mulmACA : interchange mul mul.
+Proof. by move=> x y z t; rewrite -!mulmA (mulmCA y). Qed.
+End Commutative.
+
+Section Mul.
+Variable mul : mul_law idm.
+Lemma mul0m : left_zero idm mul. Proof. by case mul. Qed.
+Lemma mulm0 : right_zero idm mul. Proof. by case mul. Qed.
+End Mul.
+
+Section Add.
+Variables (mul : T -> T -> T) (add : add_law idm mul).
+Lemma addmA : associative add. Proof. exact: mulmA. Qed.
+Lemma addmC : commutative add. Proof. exact: mulmC. Qed.
+Lemma addmCA : left_commutative add. Proof. exact: mulmCA. Qed.
+Lemma addmAC : right_commutative add. Proof. exact: mulmAC. Qed.
+Lemma add0m : left_id idm add. Proof. exact: mul1m. Qed.
+Lemma addm0 : right_id idm add. Proof. exact: mulm1. Qed.
+Lemma mulm_addl : left_distributive mul add. Proof. by case add. Qed.
+Lemma mulm_addr : right_distributive mul add. Proof. by case add. Qed.
+End Add.
+
+Definition simpm := (mulm1, mulm0, mul1m, mul0m, mulmA).
+
+End Theory.
+
+End Theory.
+Include Theory.
+
+End Monoid.
+Export Monoid.Exports.
+
+Section PervasiveMonoids.
+
+Import Monoid.
+
+Canonical andb_monoid := Law andbA andTb andbT.
+Canonical andb_comoid := ComLaw andbC.
+
+Canonical andb_muloid := MulLaw andFb andbF.
+Canonical orb_monoid := Law orbA orFb orbF.
+Canonical orb_comoid := ComLaw orbC.
+Canonical orb_muloid := MulLaw orTb orbT.
+Canonical addb_monoid := Law addbA addFb addbF.
+Canonical addb_comoid := ComLaw addbC.
+Canonical orb_addoid := AddLaw andb_orl andb_orr.
+Canonical andb_addoid := AddLaw orb_andl orb_andr.
+Canonical addb_addoid := AddLaw andb_addl andb_addr.
+
+Canonical addn_monoid := Law addnA add0n addn0.
+Canonical addn_comoid := ComLaw addnC.
+Canonical muln_monoid := Law mulnA mul1n muln1.
+Canonical muln_comoid := ComLaw mulnC.
+Canonical muln_muloid := MulLaw mul0n muln0.
+Canonical addn_addoid := AddLaw mulnDl mulnDr.
+
+Canonical cat_monoid T := Law (@catA T) (@cat0s T) (@cats0 T).
+
+End PervasiveMonoids.
+Delimit Scope big_scope with BIG.
+Open Scope big_scope.
+
+(* The bigbody wrapper is a workaround for a quirk of the Coq pretty-printer, *)
+(* which would fail to redisplay the \big notation when the <general_term> or *)
+(* <condition> do not depend on the bound index. The BigBody constructor *)
+(* packages both in in a term in which i occurs; it also depends on the *)
+(* iterated <op>, as this can give more information on the expected type of *)
+(* the <general_term>, thus allowing for the insertion of coercions. *)
+CoInductive bigbody R I := BigBody of I & (R -> R -> R) & bool & R.
+
+Definition applybig {R I} (body : bigbody R I) x :=
+ let: BigBody _ op b v := body in if b then op v x else x.
+
+Definition reducebig R I idx r (body : I -> bigbody R I) :=
+ foldr (applybig \o body) idx r.
+
+Module Type BigOpSig.
+Parameter bigop : forall R I, R -> seq I -> (I -> bigbody R I) -> R.
+Axiom bigopE : bigop = reducebig.
+End BigOpSig.
+
+Module BigOp : BigOpSig.
+Definition bigop := reducebig.
+Lemma bigopE : bigop = reducebig. Proof. by []. Qed.
+End BigOp.
+
+Notation bigop := BigOp.bigop (only parsing).
+Canonical bigop_unlock := Unlockable BigOp.bigopE.
+
+Definition index_iota m n := iota m (n - m).
+
+Definition index_enum (T : finType) := Finite.enum T.
+
+Lemma mem_index_iota m n i : i \in index_iota m n = (m <= i < n).
+Admitted.
+
+Lemma mem_index_enum T i : i \in index_enum T.
+Admitted.
+
+Hint Resolve mem_index_enum.
+
+(*
+Lemma filter_index_enum T P : filter P (index_enum T) = enum P.
+Proof. by []. Qed.
+*)
+
+Notation "\big [ op / idx ]_ ( i <- r | P ) F" :=
+ (bigop idx r (fun i => BigBody i op P%B F)) : big_scope.
+Notation "\big [ op / idx ]_ ( i <- r ) F" :=
+ (bigop idx r (fun i => BigBody i op true F)) : big_scope.
+Notation "\big [ op / idx ]_ ( m <= i < n | P ) F" :=
+ (bigop idx (index_iota m n) (fun i : nat => BigBody i op P%B F))
+ : big_scope.
+Notation "\big [ op / idx ]_ ( m <= i < n ) F" :=
+ (bigop idx (index_iota m n) (fun i : nat => BigBody i op true F))
+ : big_scope.
+Notation "\big [ op / idx ]_ ( i | P ) F" :=
+ (bigop idx (index_enum _) (fun i => BigBody i op P%B F)) : big_scope.
+Notation "\big [ op / idx ]_ i F" :=
+ (bigop idx (index_enum _) (fun i => BigBody i op true F)) : big_scope.
+Notation "\big [ op / idx ]_ ( i : t | P ) F" :=
+ (bigop idx (index_enum _) (fun i : t => BigBody i op P%B F))
+ (only parsing) : big_scope.
+Notation "\big [ op / idx ]_ ( i : t ) F" :=
+ (bigop idx (index_enum _) (fun i : t => BigBody i op true F))
+ (only parsing) : big_scope.
+Notation "\big [ op / idx ]_ ( i < n | P ) F" :=
+ (\big[op/idx]_(i : ordinal n | P%B) F) : big_scope.
+Notation "\big [ op / idx ]_ ( i < n ) F" :=
+ (\big[op/idx]_(i : ordinal n) F) : big_scope.
+Notation "\big [ op / idx ]_ ( i 'in' A | P ) F" :=
+ (\big[op/idx]_(i | (i \in A) && P) F) : big_scope.
+Notation "\big [ op / idx ]_ ( i 'in' A ) F" :=
+ (\big[op/idx]_(i | i \in A) F) : big_scope.
+
+Notation BIG_F := (F in \big[_/_]_(i <- _ | _) F i)%pattern.
+Notation BIG_P := (P in \big[_/_]_(i <- _ | P i) _)%pattern.
+
+(* Induction loading *)
+Lemma big_load R (K K' : R -> Type) idx op I r (P : pred I) F :
+ K (\big[op/idx]_(i <- r | P i) F i) * K' (\big[op/idx]_(i <- r | P i) F i)
+ -> K' (\big[op/idx]_(i <- r | P i) F i).
+Proof. by case. Qed.
+
+Arguments big_load [R] K [K'] idx op [I].
+
+Section Elim3.
+
+Variables (R1 R2 R3 : Type) (K : R1 -> R2 -> R3 -> Type).
+Variables (id1 : R1) (op1 : R1 -> R1 -> R1).
+Variables (id2 : R2) (op2 : R2 -> R2 -> R2).
+Variables (id3 : R3) (op3 : R3 -> R3 -> R3).
+
+Hypothesis Kid : K id1 id2 id3.
+
+Lemma big_rec3 I r (P : pred I) F1 F2 F3
+ (K_F : forall i y1 y2 y3, P i -> K y1 y2 y3 ->
+ K (op1 (F1 i) y1) (op2 (F2 i) y2) (op3 (F3 i) y3)) :
+ K (\big[op1/id1]_(i <- r | P i) F1 i)
+ (\big[op2/id2]_(i <- r | P i) F2 i)
+ (\big[op3/id3]_(i <- r | P i) F3 i).
+Proof. by rewrite unlock; elim: r => //= i r; case: ifP => //; apply: K_F. Qed.
+
+Hypothesis Kop : forall x1 x2 x3 y1 y2 y3,
+ K x1 x2 x3 -> K y1 y2 y3-> K (op1 x1 y1) (op2 x2 y2) (op3 x3 y3).
+Lemma big_ind3 I r (P : pred I) F1 F2 F3
+ (K_F : forall i, P i -> K (F1 i) (F2 i) (F3 i)) :
+ K (\big[op1/id1]_(i <- r | P i) F1 i)
+ (\big[op2/id2]_(i <- r | P i) F2 i)
+ (\big[op3/id3]_(i <- r | P i) F3 i).
+Proof. by apply: big_rec3 => i x1 x2 x3 /K_F; apply: Kop. Qed.
+
+End Elim3.
+
+Arguments big_rec3 [R1 R2 R3] K [id1 op1 id2 op2 id3 op3] _ [I r P F1 F2 F3].
+Arguments big_ind3 [R1 R2 R3] K [id1 op1 id2 op2 id3 op3] _ _ [I r P F1 F2 F3].
+
+Section Elim2.
+
+Variables (R1 R2 : Type) (K : R1 -> R2 -> Type) (f : R2 -> R1).
+Variables (id1 : R1) (op1 : R1 -> R1 -> R1).
+Variables (id2 : R2) (op2 : R2 -> R2 -> R2).
+
+Hypothesis Kid : K id1 id2.
+
+Lemma big_rec2 I r (P : pred I) F1 F2
+ (K_F : forall i y1 y2, P i -> K y1 y2 ->
+ K (op1 (F1 i) y1) (op2 (F2 i) y2)) :
+ K (\big[op1/id1]_(i <- r | P i) F1 i) (\big[op2/id2]_(i <- r | P i) F2 i).
+Proof. by rewrite unlock; elim: r => //= i r; case: ifP => //; apply: K_F. Qed.
+
+Hypothesis Kop : forall x1 x2 y1 y2,
+ K x1 x2 -> K y1 y2 -> K (op1 x1 y1) (op2 x2 y2).
+Lemma big_ind2 I r (P : pred I) F1 F2 (K_F : forall i, P i -> K (F1 i) (F2 i)) :
+ K (\big[op1/id1]_(i <- r | P i) F1 i) (\big[op2/id2]_(i <- r | P i) F2 i).
+Proof. by apply: big_rec2 => i x1 x2 /K_F; apply: Kop. Qed.
+
+Hypotheses (f_op : {morph f : x y / op2 x y >-> op1 x y}) (f_id : f id2 = id1).
+Lemma big_morph I r (P : pred I) F :
+ f (\big[op2/id2]_(i <- r | P i) F i) = \big[op1/id1]_(i <- r | P i) f (F i).
+Proof. by rewrite unlock; elim: r => //= i r <-; rewrite -f_op -fun_if. Qed.
+
+End Elim2.
+
+Arguments big_rec2 [R1 R2] K [id1 op1 id2 op2] _ [I r P F1 F2].
+Arguments big_ind2 [R1 R2] K [id1 op1 id2 op2] _ _ [I r P F1 F2].
+Arguments big_morph [R1 R2] f [id1 op1 id2 op2] _ _ [I].
+
+Section Elim1.
+
+Variables (R : Type) (K : R -> Type) (f : R -> R).
+Variables (idx : R) (op op' : R -> R -> R).
+
+Hypothesis Kid : K idx.
+
+Lemma big_rec I r (P : pred I) F
+ (Kop : forall i x, P i -> K x -> K (op (F i) x)) :
+ K (\big[op/idx]_(i <- r | P i) F i).
+Proof. by rewrite unlock; elim: r => //= i r; case: ifP => //; apply: Kop. Qed.
+
+Hypothesis Kop : forall x y, K x -> K y -> K (op x y).
+Lemma big_ind I r (P : pred I) F (K_F : forall i, P i -> K (F i)) :
+ K (\big[op/idx]_(i <- r | P i) F i).
+Proof. by apply: big_rec => // i x /K_F /Kop; apply. Qed.
+
+Hypothesis Kop' : forall x y, K x -> K y -> op x y = op' x y.
+Lemma eq_big_op I r (P : pred I) F (K_F : forall i, P i -> K (F i)) :
+ \big[op/idx]_(i <- r | P i) F i = \big[op'/idx]_(i <- r | P i) F i.
+Proof.
+by elim/(big_load K): _; elim/big_rec2: _ => // i _ y Pi [Ky <-]; auto.
+Qed.
+
+Hypotheses (fM : {morph f : x y / op x y}) (f_id : f idx = idx).
+Lemma big_endo I r (P : pred I) F :
+ f (\big[op/idx]_(i <- r | P i) F i) = \big[op/idx]_(i <- r | P i) f (F i).
+Proof. exact: big_morph. Qed.
+
+End Elim1.
+
+Arguments big_rec [R] K [idx op] _ [I r P F].
+Arguments big_ind [R] K [idx op] _ _ [I r P F].
+Arguments eq_big_op [R] K [idx op] op' _ _ _ [I].
+Arguments big_endo [R] f [idx op] _ _ [I].
+
+(* zmodp -------------------------------------------------------------------- *)
+
+Lemma ord1 : all_equal_to (@Ordinal 1 0 is_true_true : 'I_1).
+Admitted.
diff --git a/test-suite/prerequisite/ssr_ssrsyntax1.v b/test-suite/prerequisite/ssr_ssrsyntax1.v
new file mode 100644
index 000000000..2b404e2de
--- /dev/null
+++ b/test-suite/prerequisite/ssr_ssrsyntax1.v
@@ -0,0 +1,36 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require ssreflect.
+Require Import Arith.
+
+Goal (forall a b, a + b = b + a).
+intros.
+rewrite plus_comm, plus_comm.
+split.
+Abort.
+
+Module Foo.
+Import ssreflect.
+
+Goal (forall a b, a + b = b + a).
+intros.
+rewrite 2![_ + _]plus_comm.
+split.
+Abort.
+End Foo.
+
+Goal (forall a b, a + b = b + a).
+intros.
+rewrite plus_comm, plus_comm.
+split.
+Abort.
diff --git a/test-suite/ssr/absevarprop.v b/test-suite/ssr/absevarprop.v
new file mode 100644
index 000000000..fa1de0095
--- /dev/null
+++ b/test-suite/ssr/absevarprop.v
@@ -0,0 +1,96 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect ssrbool ssrfun.
+Require Import TestSuite.ssr_mini_mathcomp.
+
+Lemma test15: forall (y : nat) (x : 'I_2), y < 1 -> val x = y -> Some x = insub y.
+move=> y x le_1 defx; rewrite insubT ?(leq_trans le_1) // => ?.
+by congr (Some _); apply: val_inj=> /=; exact: defx.
+Qed.
+
+Axiom P : nat -> Prop.
+Axiom Q : forall n, P n -> Prop.
+Definition R := fun (x : nat) (p : P x) m (q : P (x+1)) => m > 0.
+
+Inductive myEx : Type := ExI : forall n (pn : P n) pn', Q n pn -> R n pn n pn' -> myEx.
+
+Variable P1 : P 1.
+Variable P11 : P (1 + 1).
+Variable Q1 : forall P1, Q 1 P1.
+
+Lemma testmE1 : myEx.
+Proof.
+apply: ExI 1 _ _ _ _.
+ match goal with |- P 1 => exact: P1 | _ => fail end.
+ match goal with |- P (1+1) => exact: P11 | _ => fail end.
+ match goal with |- forall p : P 1, Q 1 p => move=> *; exact: Q1 | _ => fail end.
+match goal with |- forall (p : P 1) (q : P (1+1)), is_true (R 1 p 1 q) => done | _ => fail end.
+Qed.
+
+Lemma testE2 : exists y : { x | P x }, sval y = 1.
+Proof.
+apply: ex_intro (exist _ 1 _) _.
+ match goal with |- P 1 => exact: P1 | _ => fail end.
+match goal with |- forall p : P 1, @sval _ _ (@exist _ _ 1 p) = 1 => done | _ => fail end.
+Qed.
+
+Lemma testE3 : exists y : { x | P x }, sval y = 1.
+Proof.
+have := (ex_intro _ (exist _ 1 _) _); apply.
+ match goal with |- P 1 => exact: P1 | _ => fail end.
+match goal with |- forall p : P 1, @sval _ _ (@exist _ _ 1 p) = 1 => done | _ => fail end.
+Qed.
+
+Lemma testE4 : P 2 -> exists y : { x | P x }, sval y = 2.
+Proof.
+move=> P2; apply: ex_intro (exist _ 2 _) _.
+match goal with |- @sval _ _ (@exist _ _ 2 P2) = 2 => done | _ => fail end.
+Qed.
+
+Hint Resolve P1.
+
+Lemma testmE12 : myEx.
+Proof.
+apply: ExI 1 _ _ _ _.
+ match goal with |- P (1+1) => exact: P11 | _ => fail end.
+ match goal with |- Q 1 P1 => exact: Q1 | _ => fail end.
+match goal with |- forall (q : P (1+1)), is_true (R 1 P1 1 q) => done | _ => fail end.
+Qed.
+
+Create HintDb SSR.
+
+Hint Resolve P11 : SSR.
+
+Ltac ssrautoprop := trivial with SSR.
+
+Lemma testmE13 : myEx.
+Proof.
+apply: ExI 1 _ _ _ _.
+ match goal with |- Q 1 P1 => exact: Q1 | _ => fail end.
+match goal with |- is_true (R 1 P1 1 P11) => done | _ => fail end.
+Qed.
+
+Definition R1 := fun (x : nat) (p : P x) m (q : P (x+1)) (r : Q x p) => m > 0.
+
+Inductive myEx1 : Type :=
+ ExI1 : forall n (pn : P n) pn' (q : Q n pn), R1 n pn n pn' q -> myEx1.
+
+Hint Resolve (Q1 P1) : SSR.
+
+(* tests that goals in prop are solved in the right order, propagating instantiations,
+ thus the goal Q 1 ?p1 is faced by trivial after ?p1, and is thus evar free *)
+Lemma testmE14 : myEx1.
+Proof.
+apply: ExI1 1 _ _ _ _.
+match goal with |- is_true (R1 1 P1 1 P11 (Q1 P1)) => done | _ => fail end.
+Qed.
diff --git a/test-suite/ssr/abstract_var2.v b/test-suite/ssr/abstract_var2.v
new file mode 100644
index 000000000..7c57d2024
--- /dev/null
+++ b/test-suite/ssr/abstract_var2.v
@@ -0,0 +1,25 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+Require Import ssreflect.
+
+Set Implicit Arguments.
+
+Axiom P : nat -> nat -> Prop.
+
+Axiom tr :
+ forall x y z, P x y -> P y z -> P x z.
+
+Lemma test a b c : P a c -> P a b.
+Proof.
+intro H.
+Fail have [: s1 s2] H1 : P a b := @tr _ _ _ s1 s2.
+have [: w s1 s2] H1 : P a b := @tr _ w _ s1 s2.
+Abort.
diff --git a/test-suite/ssr/binders.v b/test-suite/ssr/binders.v
new file mode 100644
index 000000000..97b7d830f
--- /dev/null
+++ b/test-suite/ssr/binders.v
@@ -0,0 +1,55 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool TestSuite.ssr_mini_mathcomp.
+
+Lemma test (x : bool) : True.
+have H1 x := x.
+have (x) := x => H2.
+have H3 T (x : T) := x.
+have ? : bool := H1 _ x.
+have ? : bool := H2 _ x.
+have ? : bool := H3 _ x.
+have ? (z : bool) : forall y : bool, z = z := fun y => refl_equal _.
+have ? w : w = w := @refl_equal nat w.
+have ? y : true by [].
+have ? (z : bool) : z = z.
+ exact: (@refl_equal _ z).
+have ? (z w : bool) : z = z by exact: (@refl_equal _ z).
+have H w (a := 3) (_ := 4) : w && true = w.
+ by rewrite andbT.
+exact I.
+Qed.
+
+Lemma test1 : True.
+suff (x : bool): x = x /\ True.
+ by move/(_ true); case=> _.
+split; first by exact: (@refl_equal _ x).
+suff H y : y && true = y /\ True.
+ by case: (H true).
+suff H1 /= : true && true /\ True.
+ by rewrite andbT; split; [exact: (@refl_equal _ y) | exact: I].
+match goal with |- is_true true /\ True => idtac end.
+by split.
+Qed.
+
+Lemma foo n : n >= 0.
+have f i (j := i + n) : j < n.
+ match goal with j := i + n |- _ => idtac end.
+Undo 2.
+suff f i (j := i + n) : j < n.
+ done.
+match goal with j := i + n |- _ => idtac end.
+Undo 3.
+done.
+Qed.
diff --git a/test-suite/ssr/binders_of.v b/test-suite/ssr/binders_of.v
new file mode 100644
index 000000000..69b52eace
--- /dev/null
+++ b/test-suite/ssr/binders_of.v
@@ -0,0 +1,23 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+
+Require Import ssreflect.
+Require Import TestSuite.ssr_mini_mathcomp.
+
+Lemma test1 : True.
+have f of seq nat & nat : nat.
+ exact 3.
+have g of nat := 3.
+have h of nat : nat := 3.
+have _ : f [::] 3 = g 3 + h 4.
+Admitted.
diff --git a/test-suite/ssr/caseview.v b/test-suite/ssr/caseview.v
new file mode 100644
index 000000000..94b064b02
--- /dev/null
+++ b/test-suite/ssr/caseview.v
@@ -0,0 +1,17 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+
+
+Lemma test (A B : Prop) : A /\ B -> True.
+Proof. by case=> _ /id _. Qed.
diff --git a/test-suite/ssr/congr.v b/test-suite/ssr/congr.v
new file mode 100644
index 000000000..7e60b04a6
--- /dev/null
+++ b/test-suite/ssr/congr.v
@@ -0,0 +1,34 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool TestSuite.ssr_mini_mathcomp.
+
+Lemma test1 : forall a b : nat, a == b -> a == 0 -> b == 0.
+Proof. move=> a b Eab Eac; congr (_ == 0) : Eac; exact: eqP Eab. Qed.
+
+Definition arrow A B := A -> B.
+
+Lemma test2 : forall a b : nat, a == b -> arrow (a == 0) (b == 0).
+Proof. move=> a b Eab; congr (_ == 0); exact: eqP Eab. Qed.
+
+Definition equals T (A B : T) := A = B.
+
+Lemma test3 : forall a b : nat, a = b -> equals nat (a + b) (b + b).
+Proof. move=> a b E; congr (_ + _); exact E. Qed.
+
+Variable S : eqType.
+Variable f : nat -> S.
+Coercion f : nat >-> Equality.sort.
+
+Lemma test4 : forall a b : nat, b = a -> @eq S (b + b) (a + a).
+Proof. move=> a b Eba; congr (_ + _); exact: Eba. Qed.
diff --git a/test-suite/ssr/deferclear.v b/test-suite/ssr/deferclear.v
new file mode 100644
index 000000000..85353dadf
--- /dev/null
+++ b/test-suite/ssr/deferclear.v
@@ -0,0 +1,37 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+
+Require Import ssrbool TestSuite.ssr_mini_mathcomp.
+
+Variable T : Type.
+
+Lemma test0 : forall a b c d : T, True.
+Proof. by move=> a b {a} a c; exact I. Qed.
+
+Variable P : T -> Prop.
+
+Lemma test1 : forall a b c : T, P a -> forall d : T, True.
+Proof. move=> a b {a} a _ d; exact I. Qed.
+
+Definition Q := forall x y : nat, x = y.
+Axiom L : 0 = 0 -> Q.
+Axiom L' : 0 = 0 -> forall x y : nat, x = y.
+Lemma test3 : Q.
+by apply/L.
+Undo.
+rewrite /Q.
+by apply/L.
+Undo 2.
+by apply/L'.
+Qed.
diff --git a/test-suite/ssr/dependent_type_err.v b/test-suite/ssr/dependent_type_err.v
new file mode 100644
index 000000000..a5789d8dd
--- /dev/null
+++ b/test-suite/ssr/dependent_type_err.v
@@ -0,0 +1,20 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrfun ssrbool TestSuite.ssr_mini_mathcomp.
+
+Lemma ltn_leq_trans : forall n m p : nat, m < n -> n <= p -> m < p.
+move=> n m p Hmn Hnp; rewrite -ltnS.
+Fail rewrite (_ : forall n0 m0 p0 : nat, m0 <= n0 -> n0 < p0 -> m0 < p0).
+Fail rewrite leq_ltn_trans.
+Admitted.
diff --git a/test-suite/ssr/derive_inversion.v b/test-suite/ssr/derive_inversion.v
new file mode 100644
index 000000000..abf63a20c
--- /dev/null
+++ b/test-suite/ssr/derive_inversion.v
@@ -0,0 +1,29 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+Require Import ssreflect ssrbool.
+
+Set Implicit Arguments.
+
+ Inductive wf T : bool -> option T -> Type :=
+ | wf_f : wf false None
+ | wf_t : forall x, wf true (Some x).
+
+ Derive Inversion wf_inv with (forall T b (o : option T), wf b o) Sort Prop.
+
+ Lemma Problem T b (o : option T) :
+ wf b o ->
+ match b with
+ | true => exists x, o = Some x
+ | false => o = None
+ end.
+ Proof.
+ by case: b; elim/wf_inv=> //; case: o=> // a *; exists a.
+ Qed.
diff --git a/test-suite/ssr/elim.v b/test-suite/ssr/elim.v
new file mode 100644
index 000000000..908249a36
--- /dev/null
+++ b/test-suite/ssr/elim.v
@@ -0,0 +1,279 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool ssrfun TestSuite.ssr_mini_mathcomp.
+Axiom daemon : False. Ltac myadmit := case: daemon.
+
+(* Ltac debugging feature: recursive elim + eq generation *)
+Lemma testL1 : forall A (s : seq A), s = s.
+Proof.
+move=> A s; elim branch: s => [|x xs _].
+match goal with _ : _ = [::] |- [::] = [::] => move: branch => // | _ => fail end.
+match goal with _ : _ = _ :: _ |- _ :: _ = _ :: _ => move: branch => // | _ => fail end.
+Qed.
+
+(* The same but with explicit eliminator and a conflict in the intro pattern *)
+Lemma testL2 : forall A (s : seq A), s = s.
+Proof.
+move=> A s; elim/last_ind branch: s => [|x s _].
+match goal with _ : _ = [::] |- [::] = [::] => move: branch => // | _ => fail end.
+match goal with _ : _ = rcons _ _ |- rcons _ _ = rcons _ _ => move: branch => // | _ => fail end.
+Qed.
+
+(* The same but without names for variables involved in the generated eq *)
+Lemma testL3 : forall A (s : seq A), s = s.
+Proof.
+move=> A s; elim branch: s; move: (s) => _.
+match goal with _ : _ = [::] |- [::] = [::] => move: branch => // | _ => fail end.
+move=> _; match goal with _ : _ = _ :: _ |- _ :: _ = _ :: _ => move: branch => // | _ => fail end.
+Qed.
+
+Inductive foo : Type := K1 : foo | K2 : foo -> foo -> foo | K3 : (nat -> foo) -> foo.
+
+(* The same but with more intros to be done *)
+Lemma testL4 : forall (o : foo), o = o.
+Proof.
+move=> o; elim branch: o.
+match goal with _ : _ = K1 |- K1 = K1 => move: branch => // | _ => fail end.
+move=> _; match goal with _ : _ = K2 _ _ |- K2 _ _ = K2 _ _ => move: branch => // | _ => fail end.
+move=> _; match goal with _ : _ = K3 _ |- K3 _ = K3 _ => move: branch => // | _ => fail end.
+Qed.
+
+(* Occurrence counting *)
+Lemma testO1: forall (b : bool), b = b.
+Proof.
+move=> b; case: (b) / idP.
+match goal with |- is_true b -> true = true => done | _ => fail end.
+match goal with |- ~ is_true b -> false = false => done | _ => fail end.
+Qed.
+
+(* The same but only the second occ *)
+Lemma testO2: forall (b : bool), b = b.
+Proof.
+move=> b; case: {2}(b) / idP.
+match goal with |- is_true b -> b = true => done | _ => fail end.
+match goal with |- ~ is_true b -> b = false => move/(introF idP) => // | _ => fail end.
+Qed.
+
+(* The same but with eq generation *)
+Lemma testO3: forall (b : bool), b = b.
+Proof.
+move=> b; case E: {2}(b) / idP.
+match goal with _ : is_true b, _ : b = true |- b = true => move: E => _; done | _ => fail end.
+match goal with H : ~ is_true b, _ : b = false |- b = false => move: E => _; move/(introF idP): H => // | _ => fail end.
+Qed.
+
+(* Views *)
+Lemma testV1 : forall A (s : seq A), s = s.
+Proof.
+move=> A s; case/lastP E: {1}s => [| x xs].
+match goal with _ : s = [::] |- [::] = s => symmetry; exact E | _ => fail end.
+match goal with _ : s = rcons x xs |- rcons _ _ = s => symmetry; exact E | _ => fail end.
+Qed.
+
+Lemma testV2 : forall A (s : seq A), s = s.
+Proof.
+move=> A s; case/lastP E: s => [| x xs].
+match goal with _ : s = [::] |- [::] = [::] => done | _ => fail end.
+match goal with _ : s = rcons x xs |- rcons _ _ = rcons _ _ => done | _ => fail end.
+Qed.
+
+Lemma testV3 : forall A (s : seq A), s = s.
+Proof.
+move=> A s; case/lastP: s => [| x xs].
+match goal with |- [::] = [::] => done | _ => fail end.
+match goal with |- rcons _ _ = rcons _ _ => done | _ => fail end.
+Qed.
+
+(* Patterns *)
+Lemma testP1: forall (x y : nat), (y == x) && (y == x) -> y == x.
+move=> x y; elim: {2}(_ == _) / eqP.
+match goal with |- (y = x -> is_true ((y == x) && true) -> is_true (y == x)) => move=> -> // | _ => fail end.
+match goal with |- (y <> x -> is_true ((y == x) && false) -> is_true (y == x)) => move=> _; rewrite andbC // | _ => fail end.
+Qed.
+
+(* The same but with an implicit pattern *)
+Lemma testP2 : forall (x y : nat), (y == x) && (y == x) -> y == x.
+move=> x y; elim: {2}_ / eqP.
+match goal with |- (y = x -> is_true ((y == x) && true) -> is_true (y == x)) => move=> -> // | _ => fail end.
+match goal with |- (y <> x -> is_true ((y == x) && false) -> is_true (y == x)) => move=> _; rewrite andbC // | _ => fail end.
+Qed.
+
+(* The same but with an eq generation switch *)
+Lemma testP3 : forall (x y : nat), (y == x) && (y == x) -> y == x.
+move=> x y; elim E: {2}_ / eqP.
+match goal with _ : y = x |- (is_true ((y == x) && true) -> is_true (y == x)) => rewrite E; reflexivity | _ => fail end.
+match goal with _ : y <> x |- (is_true ((y == x) && false) -> is_true (y == x)) => rewrite E => /= H; exact H | _ => fail end.
+Qed.
+
+Inductive spec : nat -> nat -> nat -> Prop :=
+| specK : forall a b c, a = 0 -> b = 2 -> c = 4 -> spec a b c.
+Lemma specP : spec 0 2 4. Proof. by constructor. Qed.
+
+Lemma testP4 : (1+1) * 4 = 2 + (1+1) + (2 + 2).
+Proof.
+case: specP => a b c defa defb defc.
+match goal with |- (a.+1 + a.+1) * c = b + (a.+1 + a.+1) + (b + b) => subst; done | _ => fail end.
+Qed.
+
+Lemma testP5 : (1+1) * 4 = 2 + (1+1) + (2 + 2).
+Proof.
+case: (1 + 1) _ / specP => a b c defa defb defc.
+match goal with |- b * c = a.+2 + b + (a.+2 + a.+2) => subst; done | _ => fail end.
+Qed.
+
+Lemma testP6 : (1+1) * 4 = 2 + (1+1) + (2 + 2).
+Proof.
+case: {2}(1 + 1) _ / specP => a b c defa defb defc.
+match goal with |- (a.+1 + a.+1) * c = a.+2 + b + (a.+2 + a.+2) => subst; done | _ => fail end.
+Qed.
+
+Lemma testP7 : (1+1) * 4 = 2 + (1+1) + (2 + 2).
+Proof.
+case: _ (1 + 1) (2 + _) / specP => a b c defa defb defc.
+match goal with |- b * a.+4 = c + c => subst; done | _ => fail end.
+Qed.
+
+Lemma testP8 : (1+1) * 4 = 2 + (1+1) + (2 + 2).
+Proof.
+case E: (1 + 1) (2 + _) / specP=> [a b c defa defb defc].
+match goal with |- b * a.+4 = c + c => subst; done | _ => fail end.
+Qed.
+
+Variables (T : Type) (tr : T -> T).
+
+Inductive exec (cf0 cf1 : T) : seq T -> Prop :=
+| exec_step : tr cf0 = cf1 -> exec cf0 cf1 [::]
+| exec_star : forall cf2 t, tr cf0 = cf2 ->
+ exec cf2 cf1 t -> exec cf0 cf1 (cf2 :: t).
+
+Inductive execr (cf0 cf1 : T) : seq T -> Prop :=
+| execr_step : tr cf0 = cf1 -> execr cf0 cf1 [::]
+| execr_star : forall cf2 t, execr cf0 cf2 t ->
+ tr cf2 = cf1 -> execr cf0 cf1 (t ++ [:: cf2]).
+
+Lemma execP : forall cf0 cf1 t, exec cf0 cf1 t <-> execr cf0 cf1 t.
+Proof.
+move=> cf0 cf1 t; split => [] Ecf.
+ elim: Ecf.
+ match goal with |- forall cf2 cf3 : T, tr cf2 = cf3 ->
+ execr cf2 cf3 [::] => myadmit | _ => fail end.
+ match goal with |- forall (cf2 cf3 cf4 : T) (t0 : seq T),
+ tr cf2 = cf4 -> exec cf4 cf3 t0 -> execr cf4 cf3 t0 ->
+ execr cf2 cf3 (cf4 :: t0) => myadmit | _ => fail end.
+elim: Ecf.
+ match goal with |- forall cf2 : T,
+ tr cf0 = cf2 -> exec cf0 cf2 [::] => myadmit | _ => fail end.
+match goal with |- forall (cf2 cf3 : T) (t0 : seq T),
+ execr cf0 cf3 t0 -> exec cf0 cf3 t0 -> tr cf3 = cf2 ->
+ exec cf0 cf2 (t0 ++ [:: cf3]) => myadmit | _ => fail end.
+Qed.
+
+Fixpoint plus (m n : nat) {struct n} : nat :=
+ match n with
+ | 0 => m
+ | S p => S (plus m p)
+ end.
+
+Definition plus_equation :
+forall m n : nat,
+ plus m n =
+ match n with
+ | 0 => m
+ | p.+1 => (plus m p).+1
+ end
+:=
+fun m n : nat =>
+match
+ n as n0
+ return
+ (forall m0 : nat,
+ plus m0 n0 =
+ match n0 with
+ | 0 => m0
+ | p.+1 => (plus m0 p).+1
+ end)
+with
+| 0 => @erefl nat
+| n0.+1 => fun m0 : nat => erefl (plus m0 n0).+1
+end m.
+
+Definition plus_rect :
+forall (m : nat) (P : nat -> nat -> Type),
+ (forall n : nat, n = 0 -> P 0 m) ->
+ (forall n p : nat,
+ n = p.+1 -> P p (plus m p) -> P p.+1 (plus m p).+1) ->
+ forall n : nat, P n (plus m n)
+:=
+fun (m : nat) (P : nat -> nat -> Type)
+ (f0 : forall n : nat, n = 0 -> P 0 m)
+ (f : forall n p : nat,
+ n = p.+1 -> P p (plus m p) -> P p.+1 (plus m p).+1) =>
+fix plus0 (n : nat) : P n (plus m n) :=
+ eq_rect_r [eta P n]
+ (let f1 := f0 n in
+ let f2 := f n in
+ match
+ n as n0
+ return
+ (n = n0 ->
+ (forall p : nat,
+ n0 = p.+1 -> P p (plus m p) -> P p.+1 (plus m p).+1) ->
+ (n0 = 0 -> P 0 m) ->
+ P n0 match n0 with
+ | 0 => m
+ | p.+1 => (plus m p).+1
+ end)
+ with
+ | 0 =>
+ fun (_ : n = 0)
+ (_ : forall p : nat,
+ 0 = p.+1 ->
+ P p (plus m p) -> P p.+1 (plus m p).+1)
+ (f4 : 0 = 0 -> P 0 m) => unkeyed (f4 (erefl 0))
+ | n0.+1 =>
+ fun (_ : n = n0.+1)
+ (f3 : forall p : nat,
+ n0.+1 = p.+1 ->
+ P p (plus m p) -> P p.+1 (plus m p).+1)
+ (_ : n0.+1 = 0 -> P 0 m) =>
+ let f5 :=
+ let p := n0 in
+ let H := erefl n0.+1 : n0.+1 = p.+1 in f3 p H in
+ unkeyed (let Hrec := plus0 n0 in f5 Hrec)
+ end (erefl n) f2 f1) (plus_equation m n).
+
+Definition plus_ind := plus_rect.
+
+Lemma exF x y z: plus (plus x y) z = plus x (plus y z).
+elim/plus_ind: z / (plus _ z).
+match goal with |- forall n : nat, n = 0 -> plus x y = plus x (plus y 0) => idtac end.
+Undo 2.
+elim/plus_ind: (plus _ z).
+match goal with |- forall n : nat, n = 0 -> plus x y = plus x (plus y 0) => idtac end.
+Undo 2.
+elim/plus_ind: {z}(plus _ z).
+match goal with |- forall n : nat, n = 0 -> plus x y = plus x (plus y 0) => idtac end.
+Undo 2.
+elim/plus_ind: {z}_.
+match goal with |- forall n : nat, n = 0 -> plus x y = plus x (plus y 0) => idtac end.
+Undo 2.
+elim/plus_ind: z / _.
+match goal with |- forall n : nat, n = 0 -> plus x y = plus x (plus y 0) => idtac end.
+ done.
+by move=> _ p _ ->.
+Qed.
+
+(* BUG elim-False *)
+Lemma testeF : False -> 1 = 0.
+Proof. by elim. Qed.
diff --git a/test-suite/ssr/elim2.v b/test-suite/ssr/elim2.v
new file mode 100644
index 000000000..c7c20d8f8
--- /dev/null
+++ b/test-suite/ssr/elim2.v
@@ -0,0 +1,74 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool TestSuite.ssr_mini_mathcomp.
+(* div fintype finfun path bigop. *)
+
+Axiom daemon : False. Ltac myadmit := case: daemon.
+
+Lemma big_load R (K K' : R -> Type) idx op I r (P : pred I) F :
+ let s := \big[op/idx]_(i <- r | P i) F i in
+ K s * K' s -> K' s.
+Proof. by move=> /= [_]. Qed.
+Arguments big_load [R] K [K' idx op I r P F].
+
+Section Elim1.
+
+Variables (R : Type) (K : R -> Type) (f : R -> R).
+Variables (idx : R) (op op' : R -> R -> R).
+
+Hypothesis Kid : K idx.
+
+Ltac ASSERT1 := match goal with |- (K idx) => myadmit end.
+Ltac ASSERT2 K := match goal with |- (forall x1 : R, R ->
+ forall y1 : R, R -> K x1 -> K y1 -> K (op x1 y1)) => myadmit end.
+
+
+Lemma big_rec I r (P : pred I) F
+ (Kop : forall i x, P i -> K x -> K (op (F i) x)) :
+ K (\big[op/idx]_(i <- r | P i) F i).
+Proof.
+elim/big_ind2: {-}_.
+ ASSERT1. ASSERT2 K. match goal with |- (forall i : I, is_true (P i) -> K (F i)) => myadmit end. Undo 4.
+elim/big_ind2: _ / {-}_.
+ ASSERT1. ASSERT2 K. match goal with |- (forall i : I, is_true (P i) -> K (F i)) => myadmit end. Undo 4.
+
+elim/big_rec2: (\big[op/idx]_(i <- r | P i) op idx (F i))
+ / (\big[op/idx]_(i <- r | P i) F i).
+ ASSERT1. match goal with |- (forall i : I, R -> forall y2 : R, is_true (P i) -> K y2 -> K (op (F i) y2)) => myadmit end. Undo 3.
+
+elim/(big_load (phantom R)): _.
+ Undo.
+
+Fail elim/big_rec2: {2}_.
+
+elim/big_rec2: (\big[op/idx]_(i <- r | P i) F i)
+ / {1}(\big[op/idx]_(i <- r | P i) F i).
+ Undo.
+
+elim/(big_load (phantom R)): _.
+Undo.
+
+Fail elim/big_rec2: _ / {2}(\big[op/idx]_(i <- r | P i) F i).
+Admitted.
+
+Definition morecomplexthannecessary A (P : A -> A -> Prop) x y := P x y.
+
+Lemma grab A (P : A -> A -> Prop) n m : (n = m) -> (P n n) -> morecomplexthannecessary A P n m.
+by move->.
+Qed.
+
+Goal forall n m, m + (n + m) = m + (n * 1 + m).
+Proof. move=> n m; elim/grab : (_ * _) / {1}n => //; exact: muln1. Qed.
+
+End Elim1.
diff --git a/test-suite/ssr/elim_pattern.v b/test-suite/ssr/elim_pattern.v
new file mode 100644
index 000000000..ef4658287
--- /dev/null
+++ b/test-suite/ssr/elim_pattern.v
@@ -0,0 +1,27 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool TestSuite.ssr_mini_mathcomp.
+Axiom daemon : False. Ltac myadmit := case: daemon.
+
+Lemma test x : (x == x) = (x + x.+1 == 2 * x + 1).
+case: (X in _ = X) / eqP => _.
+match goal with |- (x == x) = true => myadmit end.
+match goal with |- (x == x) = false => myadmit end.
+Qed.
+
+Lemma test1 x : (x == x) = (x + x.+1 == 2 * x + 1).
+elim: (x in RHS).
+match goal with |- (x == x) = _ => myadmit end.
+match goal with |- forall n, (x == x) = _ -> (x == x) = _ => myadmit end.
+Qed.
diff --git a/test-suite/ssr/first_n.v b/test-suite/ssr/first_n.v
new file mode 100644
index 000000000..4971add91
--- /dev/null
+++ b/test-suite/ssr/first_n.v
@@ -0,0 +1,21 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool.
+
+Lemma test : False -> (bool -> False -> True -> True) -> True.
+move=> F; let w := constr:(2) in apply; last w first.
+- by apply: F.
+- by apply: I.
+- by apply: true.
+Qed.
diff --git a/test-suite/ssr/gen_have.v b/test-suite/ssr/gen_have.v
new file mode 100644
index 000000000..249e006f9
--- /dev/null
+++ b/test-suite/ssr/gen_have.v
@@ -0,0 +1,174 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrfun ssrbool TestSuite.ssr_mini_mathcomp.
+Axiom daemon : False. Ltac myadmit := case: daemon.
+
+Axiom P : nat -> Prop.
+Lemma clear_test (b1 b2 : bool) : b2 = b2.
+Proof.
+(* wlog gH : (b3 := b2) / b2 = b3. myadmit. *)
+gen have {b1} H, gH : (b3 := b2) (w := erefl 3) / b2 = b3.
+ myadmit.
+Fail exact (H b1).
+exact (H b2 (erefl _)).
+Qed.
+
+
+Lemma test1 n (ngt0 : 0 < n) : P n.
+gen have lt2le, /andP[H1 H2] : n ngt0 / (0 <= n) && (n != 0).
+ match goal with |- is_true((0 <= n) && (n != 0)) => myadmit end.
+Check (lt2le : forall n : nat, 0 < n -> (0 <= n) && (n != 0)).
+Check (H1 : 0 <= n).
+Check (H2 : n != 0).
+myadmit.
+Qed.
+
+Lemma test2 n (ngt0 : 0 < n) : P n.
+gen have _, /andP[H1 H2] : n ngt0 / (0 <= n) && (n != 0).
+ match goal with |- is_true((0 <= n) && (n != 0)) => myadmit end.
+lazymatch goal with
+ | lt2le : forall n : nat, is_true(0 < n) -> is_true((0 <= n) && (n != 0))
+ |- _ => fail "not cleared"
+ | _ => idtac end.
+Check (H1 : 0 <= n).
+Check (H2 : n != 0).
+myadmit.
+Qed.
+
+Lemma test3 n (ngt0 : 0 < n) : P n.
+gen have H : n ngt0 / (0 <= n) && (n != 0).
+ match goal with |- is_true((0 <= n) && (n != 0)) => myadmit end.
+Check (H : forall n : nat, 0 < n -> (0 <= n) && (n != 0)).
+myadmit.
+Qed.
+
+Lemma test4 n (ngt0 : 0 < n) : P n.
+gen have : n ngt0 / (0 <= n) && (n != 0).
+ match goal with |- is_true((0 <= n) && (n != 0)) => myadmit end.
+move=> H.
+Check(H : forall n : nat, 0 < n -> (0 <= n) && (n != 0)).
+myadmit.
+Qed.
+
+Lemma test4bis n (ngt0 : 0 < n) : P n.
+wlog suff : n ngt0 / (0 <= n) && (n != 0); last first.
+ match goal with |- is_true((0 <= n) && (n != 0)) => myadmit end.
+move=> H.
+Check(H : forall n : nat, 0 < n -> (0 <= n) && (n != 0)).
+myadmit.
+Qed.
+
+Lemma test5 n (ngt0 : 0 < n) : P n.
+Fail gen have : / (0 <= n) && (n != 0).
+Abort.
+
+Lemma test6 n (ngt0 : 0 < n) : P n.
+gen have : n ngt0 / (0 <= n) && (n != 0) by myadmit.
+Abort.
+
+Lemma test7 n (ngt0 : 0 < n) : P n.
+Fail gen have : n / (0 <= n) && (n != 0).
+Abort.
+
+Lemma test3wlog2 n (ngt0 : 0 < n) : P n.
+gen have H : (m := n) ngt0 / (0 <= m) && (m != 0).
+ match goal with
+ ngt0 : is_true(0 < m) |- is_true((0 <= m) && (m != 0)) => myadmit end.
+Check (H : forall n : nat, 0 < n -> (0 <= n) && (n != 0)).
+myadmit.
+Qed.
+
+Lemma test3wlog3 n (ngt0 : 0 < n) : P n.
+gen have H : {n} (m := n) (n := 0) ngt0 / (0 <= m) && (m != n).
+ match goal with
+ ngt0 : is_true(n < m) |- is_true((0 <= m) && (m != n)) => myadmit end.
+Check (H : forall m n : nat, n < m -> (0 <= m) && (m != n)).
+myadmit.
+Qed.
+
+Lemma testw1 n (ngt0 : 0 < n) : n <= 0.
+wlog H : (z := 0) (m := n) ngt0 / m != 0.
+ match goal with
+ |- (forall z m,
+ is_true(z < m) -> is_true(m != 0) -> is_true(m <= z)) ->
+ is_true(n <= 0) => myadmit end.
+Check(n : nat).
+Check(m : nat).
+Check(z : nat).
+Check(ngt0 : z < m).
+Check(H : m != 0).
+myadmit.
+Qed.
+
+Lemma testw2 n (ngt0 : 0 < n) : n <= 0.
+wlog H : (m := n) (z := (X in n <= X)) ngt0 / m != z.
+ match goal with
+ |- (forall m z : nat,
+ is_true(0 < m) -> is_true(m != z) -> is_true(m <= z)) ->
+ is_true(n <= 0) => idtac end.
+Restart.
+wlog H : (m := n) (one := (X in X <= _)) ngt0 / m != one.
+ match goal with
+ |- (forall m one : nat,
+ is_true(one <= m) -> is_true(m != one) -> is_true(m <= 0)) ->
+ is_true(n <= 0) => idtac end.
+Restart.
+wlog H : {n} (m := n) (z := (X in _ <= X)) ngt0 / m != z.
+ match goal with
+ |- (forall m z : nat,
+ is_true(0 < z) -> is_true(m != z) -> is_true(m <= 0)) ->
+ is_true(n <= 0) => idtac end.
+ myadmit.
+Fail Check n.
+myadmit.
+Qed.
+
+Section Test.
+Variable x : nat.
+Definition addx y := y + x.
+
+Lemma testw3 (m n : nat) (ngt0 : 0 < n) : n <= addx x.
+wlog H : (n0 := n) (y := x) (@twoy := (id _ as X in _ <= X)) / twoy = 2 * y.
+ myadmit.
+myadmit.
+Qed.
+
+
+Definition twox := x + x.
+Definition bis := twox.
+
+Lemma testw3x n (ngt0 : 0 < n) : n + x <= twox.
+wlog H : (y := x) (@twoy := (X in _ <= X)) / twoy = 2 * y.
+ match goal with
+ |- (forall y : nat,
+ let twoy := y + y in
+ twoy = 2 * y -> is_true(n + y <= twoy)) ->
+ is_true(n + x <= twox) => myadmit end.
+Restart.
+wlog H : (y := x) (@twoy := (id _ as X in _ <= X)) / twoy = 2 * y.
+ match goal with
+ |- (forall y : nat,
+ let twoy := twox in
+ twoy = 2 * y -> is_true(n + y <= twoy)) ->
+ is_true(n + x <= twox) => myadmit end.
+myadmit.
+Qed.
+
+End Test.
+
+Lemma test_in n k (def_k : k = 0) (ngtk : k < n) : P n.
+rewrite -(add0n n) in {def_k k ngtk} (m := k) (def_m := def_k) (ngtm := ngtk).
+rewrite def_m add0n in {ngtm} (e := erefl 0 ) (ngt0 := ngtm) => {def_m}.
+myadmit.
+Qed.
diff --git a/test-suite/ssr/gen_pattern.v b/test-suite/ssr/gen_pattern.v
new file mode 100644
index 000000000..c0592e884
--- /dev/null
+++ b/test-suite/ssr/gen_pattern.v
@@ -0,0 +1,33 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool TestSuite.ssr_mini_mathcomp.
+
+Notation "( a 'in' c )" := (a + c) (only parsing) : myscope.
+Delimit Scope myscope with myscope.
+
+Notation "( a 'in' c )" := (a + c) (only parsing).
+
+Lemma foo x y : x + x.+1 = x.+1 + y.
+move: {x} (x.+1) {1}x y (x.+1 in RHS).
+ match goal with |- forall a b c d, b + a = d + c => idtac end.
+Admitted.
+
+Lemma bar x y : x + x.+1 = x.+1 + y.
+move E: ((x.+1 in y)) => w.
+ match goal with |- x + x.+1 = w => rewrite -{w}E end.
+move E: (x.+1 in y)%myscope => w.
+ match goal with |- x + x.+1 = w => rewrite -{w}E end.
+move E: ((x + y).+1 as RHS) => w.
+ match goal with |- x + x.+1 = w => rewrite -{}E -addSn end.
+Admitted.
diff --git a/test-suite/ssr/have_TC.v b/test-suite/ssr/have_TC.v
new file mode 100644
index 000000000..b3a26ed2c
--- /dev/null
+++ b/test-suite/ssr/have_TC.v
@@ -0,0 +1,50 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+
+Axiom daemon : False. Ltac myadmit := case: daemon.
+
+Class foo (T : Type) := { n : nat }.
+Instance five : foo nat := {| n := 5 |}.
+
+Definition bar T {f : foo T} m : Prop :=
+ @n _ f = m.
+
+Eval compute in (bar nat 7).
+
+Lemma a : True.
+set toto := bar _ 8.
+have titi : bar _ 5.
+ reflexivity.
+have titi2 : bar _ 5 := .
+ Fail reflexivity.
+ by myadmit.
+have totoc (H : bar _ 5) : 3 = 3 := eq_refl.
+move/totoc: nat => _.
+exact I.
+Qed.
+
+Set SsrHave NoTCResolution.
+
+Lemma a' : True.
+set toto := bar _ 8.
+have titi : bar _ 5.
+ Fail reflexivity.
+ by myadmit.
+have titi2 : bar _ 5 := .
+ Fail reflexivity.
+ by myadmit.
+have totoc (H : bar _ 5) : 3 = 3 := eq_refl.
+move/totoc: nat => _.
+exact I.
+Qed.
diff --git a/test-suite/ssr/have_transp.v b/test-suite/ssr/have_transp.v
new file mode 100644
index 000000000..1c998da71
--- /dev/null
+++ b/test-suite/ssr/have_transp.v
@@ -0,0 +1,48 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrfun ssrbool TestSuite.ssr_mini_mathcomp.
+
+
+Lemma test1 n : n >= 0.
+Proof.
+have [:s1] @h m : 'I_(n+m).+1.
+ apply: Sub 0 _.
+ abstract: s1 m.
+ by auto.
+cut (forall m, 0 < (n+m).+1); last assumption.
+rewrite [_ 1 _]/= in s1 h *.
+by [].
+Qed.
+
+Lemma test2 n : n >= 0.
+Proof.
+have [:s1] @h m : 'I_(n+m).+1 := Sub 0 (s1 m).
+ move=> m; reflexivity.
+cut (forall m, 0 < (n+m).+1); last assumption.
+by [].
+Qed.
+
+Lemma test3 n : n >= 0.
+Proof.
+Fail have [:s1] @h m : 'I_(n+m).+1 by apply: (Sub 0 (s1 m)); auto.
+have [:s1] @h m : 'I_(n+m).+1 by apply: (Sub 0); abstract: s1 m; auto.
+cut (forall m, 0 < (n+m).+1); last assumption.
+by [].
+Qed.
+
+Lemma test4 n : n >= 0.
+Proof.
+have @h m : 'I_(n+m).+1 by apply: (Sub 0); abstract auto.
+by [].
+Qed.
diff --git a/test-suite/ssr/have_view_idiom.v b/test-suite/ssr/have_view_idiom.v
new file mode 100644
index 000000000..3d6c9d980
--- /dev/null
+++ b/test-suite/ssr/have_view_idiom.v
@@ -0,0 +1,18 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool.
+
+Lemma test (a b : bool) (pab : a && b) : b.
+have {pab} /= /andP [pa -> //] /= : true && (a && b) := pab.
+Qed.
diff --git a/test-suite/ssr/havesuff.v b/test-suite/ssr/havesuff.v
new file mode 100644
index 000000000..aa1f71879
--- /dev/null
+++ b/test-suite/ssr/havesuff.v
@@ -0,0 +1,85 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+
+
+Variables P G : Prop.
+
+Lemma test1 : (P -> G) -> P -> G.
+Proof.
+move=> pg p.
+have suff {pg} H : P.
+ match goal with |- P -> G => move=> _; exact: pg p | _ => fail end.
+match goal with H : P -> G |- G => exact: H p | _ => fail end.
+Qed.
+
+Lemma test2 : (P -> G) -> P -> G.
+Proof.
+move=> pg p.
+have suffices {pg} H : P.
+ match goal with |- P -> G => move=> _; exact: pg p | _ => fail end.
+match goal with H : P -> G |- G => exact: H p | _ => fail end.
+Qed.
+
+Lemma test3 : (P -> G) -> P -> G.
+Proof.
+move=> pg p.
+suff have {pg} H : P.
+ match goal with H : P |- G => exact: pg H | _ => fail end.
+match goal with |- (P -> G) -> G => move=> H; exact: H p | _ => fail end.
+Qed.
+
+Lemma test4 : (P -> G) -> P -> G.
+Proof.
+move=> pg p.
+suffices have {pg} H: P.
+ match goal with H : P |- G => exact: pg H | _ => fail end.
+match goal with |- (P -> G) -> G => move=> H; exact: H p | _ => fail end.
+Qed.
+
+(*
+Lemma test5 : (P -> G) -> P -> G.
+Proof.
+move=> pg p.
+suff have {pg} H : P := pg H.
+match goal with |- (P -> G) -> G => move=> H; exact: H p | _ => fail end.
+Qed.
+*)
+
+(*
+Lemma test6 : (P -> G) -> P -> G.
+Proof.
+move=> pg p.
+suff have {pg} H := pg H.
+match goal with |- (P -> G) -> G => move=> H; exact: H p | _ => fail end.
+Qed.
+*)
+
+Lemma test7 : (P -> G) -> P -> G.
+Proof.
+move=> pg p.
+have suff {pg} H : P := pg.
+match goal with H : P -> G |- G => exact: H p | _ => fail end.
+Qed.
+
+Lemma test8 : (P -> G) -> P -> G.
+Proof.
+move=> pg p.
+have suff {pg} H := pg.
+match goal with H : P -> G |- G => exact: H p | _ => fail end.
+Qed.
+
+Goal forall x y : bool, x = y -> x = y.
+move=> x y E.
+by have {x E} -> : x = y by [].
+Qed.
diff --git a/test-suite/ssr/if_isnt.v b/test-suite/ssr/if_isnt.v
new file mode 100644
index 000000000..b8f6b7739
--- /dev/null
+++ b/test-suite/ssr/if_isnt.v
@@ -0,0 +1,22 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+
+
+Definition unopt (x : option bool) :=
+ if x isn't Some x then false else x.
+
+Lemma test1 : unopt None = false /\
+ unopt (Some false) = false /\
+ unopt (Some true) = true.
+Proof. by auto. Qed.
diff --git a/test-suite/ssr/intro_beta.v b/test-suite/ssr/intro_beta.v
new file mode 100644
index 000000000..8a164bd80
--- /dev/null
+++ b/test-suite/ssr/intro_beta.v
@@ -0,0 +1,25 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+
+
+Axiom T : Type.
+
+Definition C (P : T -> Prop) := forall x, P x.
+
+Axiom P : T -> T -> Prop.
+
+Lemma foo : C (fun x => forall y, let z := x in P y x).
+move=> a b.
+match goal with |- (let y := _ in _) => idtac end.
+Admitted.
diff --git a/test-suite/ssr/intro_noop.v b/test-suite/ssr/intro_noop.v
new file mode 100644
index 000000000..fdc85173a
--- /dev/null
+++ b/test-suite/ssr/intro_noop.v
@@ -0,0 +1,37 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool.
+Axiom daemon : False. Ltac myadmit := case: daemon.
+
+Lemma v : True -> bool -> bool. Proof. by []. Qed.
+
+Reserved Notation " a -/ b " (at level 0).
+Reserved Notation " a -// b " (at level 0).
+Reserved Notation " a -/= b " (at level 0).
+Reserved Notation " a -//= b " (at level 0).
+
+Lemma test : forall a b c, a || b || c.
+Proof.
+move=> ---a--- - -/=- -//- -/=- -//=- b [|-].
+move: {-}a => /v/v-H; have _ := H I I.
+Fail move: {-}a {H} => /v-/v-H.
+have - -> : a = (id a) by [].
+have --> : a = (id a) by [].
+have - - _ : a = (id a) by [].
+have -{1}-> : a = (id a) by [].
+ by myadmit.
+move: a.
+case: b => -[] //.
+by myadmit.
+Qed.
diff --git a/test-suite/ssr/ipatalternation.v b/test-suite/ssr/ipatalternation.v
new file mode 100644
index 000000000..6aa9a954c
--- /dev/null
+++ b/test-suite/ssr/ipatalternation.v
@@ -0,0 +1,18 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+
+
+Lemma test1 : Prop -> Prop -> Prop -> Prop -> Prop -> True = False -> Prop -> True \/ True.
+by move=> A /= /= /= B C {A} {B} ? _ {C} {1}-> *; right.
+Qed.
diff --git a/test-suite/ssr/ltac_have.v b/test-suite/ssr/ltac_have.v
new file mode 100644
index 000000000..380e52af4
--- /dev/null
+++ b/test-suite/ssr/ltac_have.v
@@ -0,0 +1,39 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool TestSuite.ssr_mini_mathcomp.
+
+Ltac SUFF1 h t := suff h x (p := x < 0) : t.
+Ltac SUFF2 h t := suff h x (p := x < 0) : t by apply h.
+Ltac HAVE1 h t u := have h x (p := x < 0) : t := u.
+Ltac HAVE2 h t := have h x (p := x < 0) : t by [].
+Ltac HAVE3 h t := have h x (p := x < 0) : t.
+Ltac HAVES h t := have suff h : t.
+Ltac SUFFH h t := suff have h : t.
+
+Lemma foo z : z < 0.
+SUFF1 h1 (z+1 < 0).
+Undo.
+SUFF2 h2 (z < 0).
+Undo.
+HAVE1 h3 (z = z) (refl_equal z).
+Undo.
+HAVE2 h4 (z = z).
+Undo.
+HAVE3 h5 (z < 0).
+Undo.
+HAVES h6 (z < 1).
+Undo.
+SUFFH h7 (z < 1).
+Undo.
+Admitted.
diff --git a/test-suite/ssr/ltac_in.v b/test-suite/ssr/ltac_in.v
new file mode 100644
index 000000000..bcdf96dde
--- /dev/null
+++ b/test-suite/ssr/ltac_in.v
@@ -0,0 +1,26 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool TestSuite.ssr_mini_mathcomp.
+
+Set Implicit Arguments.
+Unset Strict Implicit.
+Import Prenex Implicits.
+
+(* error 1 *)
+
+Ltac subst1 H := move: H; rewrite {1} addnC; move => H.
+Ltac subst2 H := rewrite addnC in H.
+
+Goal ( forall a b: nat, b+a = 0 -> b+a=0).
+Proof. move=> a b hyp. subst1 hyp. subst2 hyp. done. Qed.
diff --git a/test-suite/ssr/move_after.v b/test-suite/ssr/move_after.v
new file mode 100644
index 000000000..a7a9afea0
--- /dev/null
+++ b/test-suite/ssr/move_after.v
@@ -0,0 +1,19 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+
+
+Goal True -> True -> True.
+move=> H1 H2.
+move H1 after H2.
+Admitted.
diff --git a/test-suite/ssr/multiview.v b/test-suite/ssr/multiview.v
new file mode 100644
index 000000000..f4e717b38
--- /dev/null
+++ b/test-suite/ssr/multiview.v
@@ -0,0 +1,58 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool TestSuite.ssr_mini_mathcomp.
+
+Goal forall m n p, n <= p -> m <= n -> m <= p.
+by move=> m n p le_n_p /leq_trans; apply.
+Undo 1.
+by move=> m n p le_n_p /leq_trans /(_ le_n_p) le_m_p; exact: le_m_p.
+Undo 1.
+by move=> m n p le_n_p /leq_trans ->.
+Qed.
+
+Goal forall P Q X : Prop, Q -> (True -> X -> Q = P) -> X -> P.
+by move=> P Q X q V /V <-.
+Qed.
+
+Lemma test0: forall a b, a && a && b -> b.
+by move=> a b; repeat move=> /andP []; move=> *.
+Qed.
+
+Lemma test1 : forall a b, a && b -> b.
+by move=> a b /andP /andP /andP [] //.
+Qed.
+
+Lemma test2 : forall a b, a && b -> b.
+by move=> a b /andP /andP /(@andP a) [] //.
+Qed.
+
+Lemma test3 : forall a b, a && (b && b) -> b.
+by move=> a b /andP [_ /andP [_ //]].
+Qed.
+
+Lemma test4: forall a b, a && b = b && a.
+by move=> a b; apply/andP/andP=> ?; apply/andP/andP/andP; rewrite andbC; apply/andP.
+Qed.
+
+Lemma test5: forall C I A O, (True -> O) -> (O -> A) -> (True -> A -> I) -> (I -> C) -> C.
+by move=> c i a o O A I C; apply/C/I/A/O.
+Qed.
+
+Lemma test6: forall A B, (A -> B) -> A -> B.
+move=> A B A_to_B a; move/A_to_B in a; exact: a.
+Qed.
+
+Lemma test7: forall A B, (A -> B) -> A -> B.
+move=> A B A_to_B a; apply A_to_B in a; exact: a.
+Qed.
diff --git a/test-suite/ssr/occarrow.v b/test-suite/ssr/occarrow.v
new file mode 100644
index 000000000..49af7ae08
--- /dev/null
+++ b/test-suite/ssr/occarrow.v
@@ -0,0 +1,23 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import TestSuite.ssr_mini_mathcomp.
+
+Lemma test1 : forall n m : nat, n = m -> m * m + n * n = n * n + n * n.
+move=> n m E; have [{2}-> _] : n * n = m * n /\ True by move: E => {1}<-.
+by move: E => {3}->.
+Qed.
+
+Lemma test2 : forall n m : nat, True /\ (n = m -> n * n = n * m).
+by move=> n m; constructor=> [|{2}->].
+Qed.
diff --git a/test-suite/ssr/patnoX.v b/test-suite/ssr/patnoX.v
new file mode 100644
index 000000000..d69f03ac3
--- /dev/null
+++ b/test-suite/ssr/patnoX.v
@@ -0,0 +1,18 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool.
+Goal forall x, x && true = x.
+move=> x.
+Fail (rewrite [X in _ && _]andbT).
+Abort.
diff --git a/test-suite/ssr/pattern.v b/test-suite/ssr/pattern.v
new file mode 100644
index 000000000..396f4f032
--- /dev/null
+++ b/test-suite/ssr/pattern.v
@@ -0,0 +1,32 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+Require Import ssrmatching.
+
+(*Set Debug SsrMatching.*)
+
+Tactic Notation "at" "[" ssrpatternarg(pat) "]" tactic(t) :=
+ let name := fresh in
+ let def_name := fresh in
+ ssrpattern pat;
+ intro name;
+ pose proof (refl_equal name) as def_name;
+ unfold name at 1 in def_name;
+ t def_name;
+ [ rewrite <- def_name | idtac.. ];
+ clear name def_name.
+
+Lemma test (H : True -> True -> 3 = 7) : 28 = 3 * 4.
+Proof.
+at [ X in X * 4 ] ltac:(fun place => rewrite -> H in place).
+- reflexivity.
+- trivial.
+- trivial.
+Qed.
diff --git a/test-suite/ssr/primproj.v b/test-suite/ssr/primproj.v
new file mode 100644
index 000000000..cf61eb436
--- /dev/null
+++ b/test-suite/ssr/primproj.v
@@ -0,0 +1,164 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+
+
+Require Import Setoid.
+Set Primitive Projections.
+
+
+Module CoqBug.
+Record foo A := Foo { foo_car : A }.
+
+Definition bar : foo _ := Foo nat 10.
+
+Variable alias : forall A, foo A -> A.
+
+Parameter e : @foo_car = alias.
+
+Goal foo_car _ bar = alias _ bar.
+Proof.
+(* Coq equally fails *)
+Fail rewrite -> e.
+Fail rewrite e at 1.
+Fail setoid_rewrite e.
+Fail setoid_rewrite e at 1.
+Set Keyed Unification.
+Fail rewrite -> e.
+Fail rewrite e at 1.
+Fail setoid_rewrite e.
+Fail setoid_rewrite e at 1.
+Admitted.
+
+End CoqBug.
+
+(* ----------------------------------------------- *)
+Require Import ssreflect.
+
+Set Primitive Projections.
+
+Module T1.
+
+Record foo A := Foo { foo_car : A }.
+
+Definition bar : foo _ := Foo nat 10.
+
+Goal foo_car _ bar = 10.
+Proof.
+match goal with
+| |- foo_car _ bar = 10 => idtac
+end.
+rewrite /foo_car.
+(*
+Fail match goal with
+| |- foo_car _ bar = 10 => idtac
+end.
+*)
+Admitted.
+
+End T1.
+
+
+Module T2.
+
+Record foo {A} := Foo { foo_car : A }.
+
+Definition bar : foo := Foo nat 10.
+
+Goal foo_car bar = 10.
+match goal with
+| |- foo_car bar = 10 => idtac
+end.
+rewrite /foo_car.
+(*
+Fail match goal with
+| |- foo_car bar = 10 => idtac
+end.
+*)
+Admitted.
+
+End T2.
+
+
+Module T3.
+
+Record foo {A} := Foo { foo_car : A }.
+
+Definition bar : foo := Foo nat 10.
+
+Goal foo_car bar = 10.
+Proof.
+rewrite -[foo_car _]/(id _).
+match goal with |- id _ = 10 => idtac end.
+Admitted.
+
+Goal foo_car bar = 10.
+Proof.
+set x := foo_car _.
+match goal with |- x = 10 => idtac end.
+Admitted.
+
+End T3.
+
+Module T4.
+
+Inductive seal {A} (f : A) := { unseal : A; seal_eq : unseal = f }.
+Arguments unseal {_ _} _.
+Arguments seal_eq {_ _} _.
+
+Record uPred : Type := IProp { uPred_holds :> Prop }.
+
+Definition uPred_or_def (P Q : uPred) : uPred :=
+ {| uPred_holds := P \/ Q |}.
+Definition uPred_or_aux : seal (@uPred_or_def). by eexists. Qed.
+Definition uPred_or := unseal uPred_or_aux.
+Definition uPred_or_eq: @uPred_or = @uPred_or_def := seal_eq uPred_or_aux.
+
+Lemma foobar (P1 P2 Q : uPred) :
+ (P1 <-> P2) -> (uPred_or P1 Q) <-> (uPred_or P2 Q).
+Proof.
+ rewrite uPred_or_eq. (* This fails. *)
+Admitted.
+
+End T4.
+
+
+Module DesignFlaw.
+
+Record foo A := Foo { foo_car : A }.
+Definition bar : foo _ := Foo nat 10.
+
+Definition app (f : foo nat -> nat) x := f x.
+
+Goal app (foo_car _) bar = 10.
+Proof.
+unfold app. (* mkApp should produce a Proj *)
+Fail set x := (foo_car _ _).
+Admitted.
+
+End DesignFlaw.
+
+
+Module Bug.
+
+Record foo A := Foo { foo_car : A }.
+
+Definition bar : foo _ := Foo nat 10.
+
+Variable alias : forall A, foo A -> A.
+
+Parameter e : @foo_car = alias.
+
+Goal foo_car _ bar = alias _ bar.
+Proof.
+Fail rewrite e. (* Issue: #86 *)
+Admitted.
+
+End Bug.
diff --git a/test-suite/ssr/rewpatterns.v b/test-suite/ssr/rewpatterns.v
new file mode 100644
index 000000000..f7993f402
--- /dev/null
+++ b/test-suite/ssr/rewpatterns.v
@@ -0,0 +1,146 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+
+Require Import ssreflect.
+Require Import ssrbool ssrfun TestSuite.ssr_mini_mathcomp.
+
+Lemma test1 : forall x y (f : nat -> nat), f (x + y).+1 = f (y + x.+1).
+by move=> x y f; rewrite [_.+1](addnC x.+1).
+Qed.
+
+Lemma test2 : forall x y f, x + y + f (y + x) + f (y + x) = x + y + f (y + x) + f (x + y).
+by move=> x y f; rewrite {2}[in f _]addnC.
+Qed.
+
+Lemma test2' : forall x y f, true && f (x * (y + x)) = true && f(x * (x + y)).
+by move=> x y f; rewrite [in f _](addnC y).
+Qed.
+
+Lemma test2'' : forall x y f, f (y + x) + f(y + x) + f(y + x) = f(x + y) + f(y + x) + f(x + y).
+by move=> x y f; rewrite {1 3}[in f _](addnC y).
+Qed.
+
+(* patterns catching bound vars not supported *)
+Lemma test2_1 : forall x y f, true && (let z := x in f (z * (y + x))) = true && f(x * (x + y)).
+by move=> x y f; rewrite [in f _](addnC x). (* put y when bound var will be OK *)
+Qed.
+
+Lemma test3 : forall x y f, x + f (x + y) (f (y + x) x) = x + f (x + y) (f (x + y) x).
+by move=> x y f; rewrite [in X in (f _ X)](addnC y).
+Qed.
+
+Lemma test3' : forall x y f, x = y -> x + f (x + x) x + f (x + x) x =
+ x + f (x + y) x + f (y + x) x.
+by move=> x y f E; rewrite {2 3}[in X in (f X _)]E.
+Qed.
+
+Lemma test3'' : forall x y f, x = y -> x + f (x + y) x + f (x + y) x =
+ x + f (x + y) x + f (y + y) x.
+by move=> x y f E; rewrite {2}[in X in (f X _)]E.
+Qed.
+
+Lemma test4 : forall x y f, x = y -> x + f (fun _ : nat => x + x) x + f (fun _ => x + x) x =
+ x + f (fun _ => x + y) x + f (fun _ => y + x) x.
+by move=> x y f E; rewrite {2 3}[in X in (f X _)]E.
+Qed.
+
+Lemma test4' : forall x y f, x = y -> x + f (fun _ _ _ : nat => x + x) x =
+ x + f (fun _ _ _ => x + y) x.
+by move=> x y f E; rewrite {2}[in X in (f X _)]E.
+Qed.
+
+Lemma test5 : forall x y f, x = y -> x + f (y + x) x + f (y + x) x =
+ x + f (x + y) x + f (y + x) x.
+by move=> x y f E; rewrite {1}[X in (f X _)]addnC.
+Qed.
+
+Lemma test3''' : forall x y f, x = y -> x + f (x + y) x + f (x + y) (x + y) =
+ x + f (x + y) x + f (y + y) (x + y).
+by move=> x y f E; rewrite {1}[in X in (f X X)]E.
+Qed.
+
+Lemma test3'''' : forall x y f, x = y -> x + f (x + y) x + f (x + y) (x + y) =
+ x + f (x + y) x + f (y + y) (y + y).
+by move=> x y f E; rewrite [in X in (f X X)]E.
+Qed.
+
+Lemma test3x : forall x y f, y+y = x+y -> x + f (x + y) x + f (x + y) (x + y) =
+ x + f (x + y) x + f (y + y) (y + y).
+by move=> x y f E; rewrite -[X in (f X X)]E.
+Qed.
+
+Lemma test6 : forall x y (f : nat -> nat), f (x + y).+1 = f (y.+1 + x).
+by move=> x y f; rewrite [(x + y) in X in (f X)]addnC.
+Qed.
+
+Lemma test7 : forall x y (f : nat -> nat), f (x + y).+1 = f (y + x.+1).
+by move=> x y f; rewrite [(x.+1 + y) as X in (f X)]addnC.
+Qed.
+
+Lemma manual x y z (f : nat -> nat -> nat) : (x + y).+1 + f (x.+1 + y) (z + (x + y).+1) = 0.
+Proof.
+rewrite [in f _]addSn.
+match goal with |- (x + y).+1 + f (x + y).+1 (z + (x + y).+1) = 0 => idtac end.
+rewrite -[X in _ = X]addn0.
+match goal with |- (x + y).+1 + f (x + y).+1 (z + (x + y).+1) = 0 + 0 => idtac end.
+rewrite -{2}[in X in _ = X](addn0 0).
+match goal with |- (x + y).+1 + f (x + y).+1 (z + (x + y).+1) = 0 + (0 + 0) => idtac end.
+rewrite [_.+1 in X in f _ X](addnC x.+1).
+match goal with |- (x + y).+1 + f (x + y).+1 (z + (y + x.+1)) = 0 + (0 + 0) => idtac end.
+rewrite [x.+1 + y as X in f X _]addnC.
+match goal with |- (x + y).+1 + f (y + x.+1) (z + (y + x.+1)) = 0 + (0 + 0) => idtac end.
+Admitted.
+
+Goal (exists x : 'I_3, x > 0).
+apply: (ex_intro _ (@Ordinal _ 2 _)).
+Admitted.
+
+Goal (forall y, 1 < y < 2 -> exists x : 'I_3, x > 0).
+move=> y; case/andP=> y_gt1 y_lt2; apply: (ex_intro _ (@Ordinal _ y _)).
+ by apply: leq_trans y_lt2 _.
+by move=> y_lt3; apply: leq_trans _ y_gt1.
+Qed.
+
+Goal (forall x y : nat, forall P : nat -> Prop, x = y -> True).
+move=> x y P E.
+have: P x -> P y by suff: x = y by move=> ?; congr (P _).
+Admitted.
+
+Goal forall a : bool, a -> true && a || false && a.
+by move=> a ?; rewrite [true && _]/= [_ && a]/= orbC [_ || _]//=.
+Qed.
+
+Goal forall a : bool, a -> true && a || false && a.
+by move=> a ?; rewrite [X in X || _]/= [X in _ || X]/= orbC [false && a as X in X || _]//=.
+Qed.
+
+Variable a : bool.
+Definition f x := x || a.
+Definition g x := f x.
+
+Goal a -> g false.
+by move=> Ha; rewrite [g _]/f orbC Ha.
+Qed.
+
+Goal a -> g false || g false.
+move=> Ha; rewrite {2}[g _]/f orbC Ha.
+match goal with |- (is_true (false || true || g false)) => done end.
+Qed.
+
+Goal a -> (a && a || true && a) && true.
+by move=> Ha; rewrite -[_ || _]/(g _) andbC /= Ha [g _]/f.
+Qed.
+
+Goal a -> (a || a) && true.
+by move=> Ha; rewrite -[in _ || _]/(f _) Ha andbC /f.
+Qed.
diff --git a/test-suite/ssr/set_lamda.v b/test-suite/ssr/set_lamda.v
new file mode 100644
index 000000000..a012ec680
--- /dev/null
+++ b/test-suite/ssr/set_lamda.v
@@ -0,0 +1,27 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool ssrfun.
+Require Import TestSuite.ssr_mini_mathcomp.
+
+Set Implicit Arguments.
+Unset Strict Implicit.
+Import Prenex Implicits.
+
+(* error 2 *)
+
+Goal (exists f: Set -> nat, f nat = 0).
+Proof. set (f:= fun _:Set =>0). by exists f. Qed.
+
+Goal (exists f: Set -> nat, f nat = 0).
+Proof. set f := (fun _:Set =>0). by exists f. Qed.
diff --git a/test-suite/ssr/set_pattern.v b/test-suite/ssr/set_pattern.v
new file mode 100644
index 000000000..3ce75e879
--- /dev/null
+++ b/test-suite/ssr/set_pattern.v
@@ -0,0 +1,64 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+
+Axiom daemon : False. Ltac myadmit := case: daemon.
+
+Ltac T1 x := match goal with |- _ => set t := (x in X in _ = X) end.
+Ltac T2 x := first [set t := (x in RHS)].
+Ltac T3 x := first [set t := (x in Y in _ = Y)|idtac].
+Ltac T4 x := set t := (x in RHS); idtac.
+Ltac T5 x := match goal with |- _ => set t := (x in RHS) | |- _ => idtac end.
+
+Require Import ssrbool TestSuite.ssr_mini_mathcomp.
+
+Open Scope nat_scope.
+
+Lemma foo x y : x.+1 = y + x.+1.
+set t := (_.+1 in RHS). match goal with |- x.+1 = y + t => rewrite /t {t} end.
+set t := (x in RHS). match goal with |- x.+1 = y + t.+1 => rewrite /t {t} end.
+set t := (x in _ = x). match goal with |- x.+1 = t => rewrite /t {t} end.
+set t := (x in X in _ = X).
+ match goal with |- x.+1 = y + t.+1 => rewrite /t {t} end.
+set t := (x in RHS). match goal with |- x.+1 = y + t.+1 => rewrite /t {t} end.
+set t := (y + (1 + x) as X in _ = X).
+ match goal with |- x.+1 = t => rewrite /t addSn add0n {t} end.
+set t := x.+1. match goal with |- t = y + t => rewrite /t {t} end.
+set t := (x).+1. match goal with |- t = y + t => rewrite /t {t} end.
+set t := ((x).+1 in X in _ = X).
+ match goal with |- x.+1 = y + t => rewrite /t {t} end.
+set t := (x.+1 in RHS). match goal with |- x.+1 = y + t => rewrite /t {t} end.
+T1 (x.+1). match goal with |- x.+1 = y + t => rewrite /t {t} end.
+T2 (x.+1). match goal with |- x.+1 = y + t => rewrite /t {t} end.
+T3 (x.+1). match goal with |- x.+1 = y + t => rewrite /t {t} end.
+T4 (x.+1). match goal with |- x.+1 = y + t => rewrite /t {t} end.
+T5 (x.+1). match goal with |- x.+1 = y + t => rewrite /t {t} end.
+rewrite [RHS]addnC.
+ match goal with |- x.+1 = x.+1 + y => rewrite -[RHS]addnC end.
+rewrite -[in RHS](@subnK 1 x.+1) //.
+ match goal with |- x.+1 = y + (x.+1 - 1 + 1) => rewrite subnK // end.
+have H : x.+1 = y by myadmit.
+set t := _.+1 in H |- *.
+ match goal with H : t = y |- t = y + t => rewrite /t {t} in H * end.
+set t := (_.+1 in X in _ + X) in H |- *.
+ match goal with H : x.+1 = y |- x.+1 = y + t => rewrite /t {t} in H * end.
+set t := 0. match goal with t := 0 |- x.+1 = y + x.+1 => clear t end.
+set t := y + _. match goal with |- x.+1 = t => rewrite /t {t} end.
+set t : nat := 0. clear t.
+set t : nat := (x in RHS).
+ match goal with |- x.+1 = y + t.+1 => rewrite /t {t} end.
+set t : nat := RHS. match goal with |- x.+1 = t => rewrite /t {t} end.
+(* set t := 0 + _. *)
+(* set t := (x).+1 in X in _ + X in H |-. *)
+(* set t := (x).+1 in X in _ = X.*)
+Admitted.
diff --git a/test-suite/ssr/ssrsyntax2.v b/test-suite/ssr/ssrsyntax2.v
new file mode 100644
index 000000000..af839fabd
--- /dev/null
+++ b/test-suite/ssr/ssrsyntax2.v
@@ -0,0 +1,20 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import TestSuite.ssr_ssrsyntax1.
+Require Import Arith.
+
+Goal (forall a b, a + b = b + a).
+intros.
+rewrite plus_comm, plus_comm.
+split.
+Qed.
diff --git a/test-suite/ssr/tc.v b/test-suite/ssr/tc.v
new file mode 100644
index 000000000..ae4589ef3
--- /dev/null
+++ b/test-suite/ssr/tc.v
@@ -0,0 +1,39 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+
+
+Class foo (A : Type) : Type := mkFoo { val : A }.
+Instance foo_pair {A B} {f1 : foo A} {f2 : foo B} : foo (A * B) | 2 :=
+ {| val := (@val _ f1, @val _ f2) |}.
+Instance foo_nat : foo nat | 3 := {| val := 0 |}.
+
+Definition id {A} (x : A) := x.
+Axiom E : forall A {f : foo A} (a : A), id a = (@val _ f).
+
+Lemma test (x : nat) : id true = true -> id x = 0.
+Proof.
+Fail move=> _; reflexivity.
+Timeout 2 rewrite E => _; reflexivity.
+Qed.
+
+Definition P {A} (x : A) : Prop := x = x.
+Axiom V : forall A {f : foo A} (x:A), P x -> P (id x).
+
+Lemma test1 (x : nat) : P x -> P (id x).
+Proof.
+move=> px.
+Timeout 2 Fail move/V: px.
+Timeout 2 move/V : (px) => _.
+move/(V nat) : px => H; exact H.
+Qed.
diff --git a/test-suite/ssr/typeof.v b/test-suite/ssr/typeof.v
new file mode 100644
index 000000000..ca121fdb3
--- /dev/null
+++ b/test-suite/ssr/typeof.v
@@ -0,0 +1,22 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+
+Ltac mycut x :=
+ let tx := type of x in
+ cut tx.
+
+Lemma test : True.
+Proof.
+by mycut I=> [ x | ]; [ exact x | exact I ].
+Qed.
diff --git a/test-suite/ssr/unfold_Opaque.v b/test-suite/ssr/unfold_Opaque.v
new file mode 100644
index 000000000..7c2b51de4
--- /dev/null
+++ b/test-suite/ssr/unfold_Opaque.v
@@ -0,0 +1,18 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+Require Import ssreflect.
+
+Definition x := 3.
+Opaque x.
+
+Goal x = 3.
+Fail rewrite /x.
+Admitted.
diff --git a/test-suite/ssr/unkeyed.v b/test-suite/ssr/unkeyed.v
new file mode 100644
index 000000000..710941c30
--- /dev/null
+++ b/test-suite/ssr/unkeyed.v
@@ -0,0 +1,31 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrfun ssrbool TestSuite.ssr_mini_mathcomp.
+
+Set Implicit Arguments.
+Unset Strict Implicit.
+Import Prenex Implicits.
+
+Lemma test0 (a b : unit) f : a = f b.
+Proof. by rewrite !unitE. Qed.
+
+Lemma phE T : all_equal_to (Phant T). Proof. by case. Qed.
+
+Lemma test1 (a b : phant nat) f : a = f b.
+Proof. by rewrite !phE. Qed.
+
+Lemma eq_phE (T : eqType) : all_equal_to (Phant T). Proof. by case. Qed.
+
+Lemma test2 (a b : phant bool) f : a = locked (f b).
+Proof. by rewrite !eq_phE. Qed.
diff --git a/test-suite/ssr/view_case.v b/test-suite/ssr/view_case.v
new file mode 100644
index 000000000..2721470c4
--- /dev/null
+++ b/test-suite/ssr/view_case.v
@@ -0,0 +1,31 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool TestSuite.ssr_mini_mathcomp.
+
+Axiom P : forall T, seq T -> Prop.
+
+Goal (forall T (s : seq T), P _ s).
+move=> T s.
+elim: s => [| x /lastP [| s] IH].
+Admitted.
+
+Goal forall x : 'I_1, x = 0 :> nat.
+move=> /ord1 -> /=; exact: refl_equal.
+Qed.
+
+Goal forall x : 'I_1, x = 0 :> nat.
+move=> x.
+move=> /ord1 -> in x |- *.
+exact: refl_equal.
+Qed.
diff --git a/test-suite/ssr/wlog_suff.v b/test-suite/ssr/wlog_suff.v
new file mode 100644
index 000000000..43a8f3b8b
--- /dev/null
+++ b/test-suite/ssr/wlog_suff.v
@@ -0,0 +1,28 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool.
+
+Lemma test b : b || ~~b.
+wlog _ : b / b = true.
+ case: b; [ by apply | by rewrite orbC ].
+wlog suff: b / b || ~~b.
+ by case: b.
+by case: b.
+Qed.
+
+Lemma test2 b c (H : c = b) : b || ~~b.
+wlog _ : b {c H} / b = true.
+ by case: b H.
+by case: b.
+Qed.
diff --git a/test-suite/ssr/wlogletin.v b/test-suite/ssr/wlogletin.v
new file mode 100644
index 000000000..64e1ea84f
--- /dev/null
+++ b/test-suite/ssr/wlogletin.v
@@ -0,0 +1,50 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool.
+Require Import TestSuite.ssr_mini_mathcomp.
+
+Variable T : Type.
+Variables P : T -> Prop.
+
+Definition f := fun x y : T => x.
+
+Lemma test1 : forall x y : T, P (f x y) -> P x.
+Proof.
+move=> x y; set fxy := f x y; move=> Pfxy.
+wlog H : @fxy Pfxy / P x.
+ match goal with |- (let fxy0 := f x y in P fxy0 -> P x -> P x) -> P x => by auto | _ => fail end.
+exact: H.
+Qed.
+
+Lemma test2 : forall x y : T, P (f x y) -> P x.
+Proof.
+move=> x y; set fxy := f x y; move=> Pfxy.
+wlog H : fxy Pfxy / P x.
+ match goal with |- (forall fxy, P fxy -> P x -> P x) -> P x => by auto | _ => fail end.
+exact: H.
+Qed.
+
+Lemma test3 : forall x y : T, P (f x y) -> P x.
+Proof.
+move=> x y; set fxy := f x y; move=> Pfxy.
+move: {1}@fxy (Pfxy) (Pfxy).
+match goal with |- (let fxy0 := f x y in P fxy0 -> P fxy -> P x) => by auto | _ => fail end.
+Qed.
+
+Lemma test4 : forall n m z: bool, n = z -> let x := n in x = m && n -> x = m && n.
+move=> n m z E x H.
+case: true.
+ by rewrite {1 2}E in (x) H |- *.
+by rewrite {1}E in x H |- *.
+Qed.
diff --git a/test-suite/ssr/wlong_intro.v b/test-suite/ssr/wlong_intro.v
new file mode 100644
index 000000000..dd80f0435
--- /dev/null
+++ b/test-suite/ssr/wlong_intro.v
@@ -0,0 +1,20 @@
+(************************************************************************)
+(* * The Coq Proof Assistant / The Coq Development Team *)
+(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *)
+(* <O___,, * (see CREDITS file for the list of authors) *)
+(* \VV/ **************************************************************)
+(* // * This file is distributed under the terms of the *)
+(* * GNU Lesser General Public License Version 2.1 *)
+(* * (see LICENSE file for the text of the license) *)
+(************************************************************************)
+
+(* (c) Copyright 2006-2016 Microsoft Corporation and Inria. *)
+
+Require Import ssreflect.
+Require Import ssrbool.
+Require Import TestSuite.ssr_mini_mathcomp.
+
+Goal (forall x y : nat, True).
+move=> x y.
+wlog suff: x y / x <= y.
+Admitted.