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Diffstat (limited to 'test-suite/bugs/opened/shouldnotfail/1596.v')
| -rw-r--r-- | test-suite/bugs/opened/shouldnotfail/1596.v | 242 |
1 files changed, 242 insertions, 0 deletions
diff --git a/test-suite/bugs/opened/shouldnotfail/1596.v b/test-suite/bugs/opened/shouldnotfail/1596.v new file mode 100644 index 00000000..766bf524 --- /dev/null +++ b/test-suite/bugs/opened/shouldnotfail/1596.v @@ -0,0 +1,242 @@ + +Require Import Relations. +Require Import FSets. +Require Import Arith. + +Lemma Bool_elim_bool : forall (b:bool),b=true \/ b=false. + destruct b;try tauto. +Qed. + +Module OrderedPair (X:OrderedType) (Y:OrderedType) <: OrderedType with +Definition t := (X.t * Y.t)%type. + Definition t := (X.t * Y.t)%type. + + Definition eq (xy1:t) (xy2:t) := + let (x1,y1) := xy1 in + let (x2,y2) := xy2 in + (X.eq x1 x2) /\ (Y.eq y1 y2). + + Definition lt (xy1:t) (xy2:t) := + let (x1,y1) := xy1 in + let (x2,y2) := xy2 in + (X.lt x1 x2) \/ ((X.eq x1 x2) /\ (Y.lt y1 y2)). + + Lemma eq_refl : forall (x:t),(eq x x). + destruct x. + unfold eq. + split;[apply X.eq_refl | apply Y.eq_refl]. + Qed. + + Lemma eq_sym : forall (x y:t),(eq x y)->(eq y x). + destruct x;destruct y;unfold eq;intro. + elim H;clear H;intros. + split;[apply X.eq_sym | apply Y.eq_sym];trivial. + Qed. + + Lemma eq_trans : forall (x y z:t),(eq x y)->(eq y z)->(eq x z). + unfold eq;destruct x;destruct y;destruct z;intros. + elim H;clear H;intros. + elim H0;clear H0;intros. + split;[eapply X.eq_trans | eapply Y.eq_trans];eauto. + Qed. + + Lemma lt_trans : forall (x y z:t),(lt x y)->(lt y z)->(lt x z). + unfold lt;destruct x;destruct y;destruct z;intros. + case H;clear H;intro. + case H0;clear H0;intro. + left. + eapply X.lt_trans;eauto. + elim H0;clear H0;intros. + left. + case (X.compare t0 t4);trivial;intros. + generalize (X.eq_sym H0);intro. + generalize (X.eq_trans e H2);intro. + elim (X.lt_not_eq H H3). + generalize (X.lt_trans l H);intro. + generalize (X.eq_sym H0);intro. + elim (X.lt_not_eq H2 H3). + elim H;clear H;intros. + case H0;clear H0;intro. + left. + case (X.compare t0 t4);trivial;intros. + generalize (X.eq_sym H);intro. + generalize (X.eq_trans H2 e);intro. + elim (X.lt_not_eq H0 H3). + generalize (X.lt_trans H0 l);intro. + generalize (X.eq_sym H);intro. + elim (X.lt_not_eq H2 H3). + elim H0;clear H0;intros. + right. + split. + eauto. + eauto. + Qed. + + Lemma lt_not_eq : forall (x y:t),(lt x y)->~(eq x y). + unfold lt, eq;destruct x;destruct y;intro;intro. + elim H0;clear H0;intros. + case H. + intro. + apply (X.lt_not_eq H2 H0). + intro. + elim H2;clear H2;intros. + apply (Y.lt_not_eq H3 H1). + Qed. + + Definition compare : forall (x y:t),(Compare lt eq x y). + destruct x;destruct y. + case (X.compare t0 t2);intro. + apply LT. + left;trivial. + case (Y.compare t1 t3);intro. + apply LT. + right. + tauto. + apply EQ. + split;trivial. + apply GT. + right;auto. + apply GT. + left;trivial. + Defined. + + Hint Immediate eq_sym. + Hint Resolve eq_refl eq_trans lt_not_eq lt_trans. +End OrderedPair. + +Module MessageSpi. + Inductive message : Set := + | MNam : nat -> message. + + Definition t := message. + + Fixpoint message_lt (m n:message) {struct m} : Prop := + match (m,n) with + | (MNam n1,MNam n2) => n1 < n2 + end. + + Module Ord <: OrderedType with Definition t := message with Definition eq := +@eq message. + Definition t := message. + Definition eq := @eq message. + Definition lt := message_lt. + + Lemma eq_refl : forall (x:t),eq x x. + unfold eq;auto. + Qed. + + Lemma eq_sym : forall (x y:t),(eq x y )->(eq y x). + unfold eq;auto. + Qed. + + Lemma eq_trans : forall (x y z:t),(eq x y)->(eq y z)->(eq x z). + unfold eq;auto;intros;congruence. + Qed. + + Lemma lt_trans : forall (x y z:t),(lt x y)->(lt y z)->(lt x z). + unfold lt. + induction x;destruct y;simpl;try tauto;destruct z;try tauto;intros. + omega. + Qed. + + Lemma lt_not_eq : forall (x y:t),(lt x y)->~(eq x y). + unfold eq;unfold lt. + induction x;destruct y;simpl;try tauto;intro;red;intro;try (discriminate +H0);injection H0;intros. + elim (lt_irrefl n);try omega. + Qed. + + Definition compare : forall (x y:t),(Compare lt eq x y). + unfold lt, eq. + induction x;destruct y;intros;try (apply LT;simpl;trivial;fail);try +(apply +GT;simpl;trivial;fail). + case (lt_eq_lt_dec n n0);intros;try (case s;clear s;intros). + apply LT;trivial. + apply EQ;trivial. + rewrite e;trivial. + apply GT;trivial. + Defined. + + Hint Immediate eq_sym. + Hint Resolve eq_refl eq_trans lt_not_eq lt_trans. + End Ord. + + Theorem eq_dec : forall (m n:message),{m=n}+{~(m=n)}. + intros. + case (Ord.compare m n);intro;[right | left | right];try (red;intro). + elim (Ord.lt_not_eq m n);auto. + rewrite e;auto. + elim (Ord.lt_not_eq n m);auto. + Defined. +End MessageSpi. + +Module MessagePair := OrderedPair MessageSpi.Ord MessageSpi.Ord. + +Module Type Hedge := FSetInterface.S with Module E := MessagePair. + +Module A (H:Hedge). + Definition hedge := H.t. + + Definition message_relation := relation MessageSpi.message. + + Definition relation_of_hedge (h:hedge) (m n:MessageSpi.message) := H.In (m,n) +h. + + Inductive hedge_synthesis_relation (h:message_relation) : message_relation := + | SynInc : forall (m n:MessageSpi.message),(h m +n)->(hedge_synthesis_relation h m n). + + Fixpoint hedge_in_synthesis (h:hedge) (m:MessageSpi.message) +(n:MessageSpi.message) {struct m} : bool := + if H.mem (m,n) h + then true + else false. + + Definition hedge_synthesis_spec (h:hedge) := hedge_synthesis_relation +(relation_of_hedge h). + + Lemma hedge_in_synthesis_impl_hedge_synthesis_spec : forall (h:hedge),forall +(m n:MessageSpi.message),(hedge_in_synthesis h m n)=true->(hedge_synthesis_spec +h m n). + unfold hedge_synthesis_spec;unfold relation_of_hedge. + induction m;simpl;intro. + elim (Bool_elim_bool (H.mem (MessageSpi.MNam n,n0) h));intros. + apply SynInc;apply H.mem_2;trivial. + rewrite H in H0. (* !! possible here !! *) + discriminate H0. + Qed. +End A. + +Module B (H:Hedge). + Definition hedge := H.t. + + Definition message_relation := relation MessageSpi.t. + + Definition relation_of_hedge (h:hedge) (m n:MessageSpi.t) := H.In (m,n) h. + + Inductive hedge_synthesis_relation (h:message_relation) : message_relation := + | SynInc : forall (m n:MessageSpi.t),(h m n)->(hedge_synthesis_relation h m +n). + + Fixpoint hedge_in_synthesis (h:hedge) (m:MessageSpi.t) (n:MessageSpi.t) +{struct m} : bool := + if H.mem (m,n) h + then true + else false. + + Definition hedge_synthesis_spec (h:hedge) := hedge_synthesis_relation +(relation_of_hedge h). + + Lemma hedge_in_synthesis_impl_hedge_synthesis_spec : forall (h:hedge),forall +(m n:MessageSpi.t),(hedge_in_synthesis h m n)=true->(hedge_synthesis_spec h m +n). + unfold hedge_synthesis_spec;unfold relation_of_hedge. + induction m;simpl;intro. + elim (Bool_elim_bool (H.mem (MessageSpi.MNam n,n0) h));intros. + apply SynInc;apply H.mem_2;trivial. + + rewrite H in H0. (* !! impossible here !! *) + discriminate H0. + Qed. +End B.
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