aboutsummaryrefslogtreecommitdiffhomepage
path: root/theories/Lists/Streams.v
diff options
context:
space:
mode:
authorGravatar delahaye <delahaye@85f007b7-540e-0410-9357-904b9bb8a0f7>2000-07-03 13:50:02 +0000
committerGravatar delahaye <delahaye@85f007b7-540e-0410-9357-904b9bb8a0f7>2000-07-03 13:50:02 +0000
commit1993e7d72cb84d8a71083fd537ada3e12fc39392 (patch)
tree3dcfd812ac4322e9871c08c812cccd54f29bb750 /theories/Lists/Streams.v
parentde3c54d963acb796ace714a6d7e9951126f007b9 (diff)
Traduction de syntaxe vers ltac
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@551 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Lists/Streams.v')
-rwxr-xr-xtheories/Lists/Streams.v31
1 files changed, 15 insertions, 16 deletions
diff --git a/theories/Lists/Streams.v b/theories/Lists/Streams.v
index 6b7ffca5e..9895af8ae 100755
--- a/theories/Lists/Streams.v
+++ b/theories/Lists/Streams.v
@@ -61,36 +61,35 @@ CoInductive EqSt : Stream->Stream->Prop :=
(* A coinduction principle *)
-Tactic Definition CoInduction [$proof] :=
- [ <:tactic:<( Cofix $proof; (Intros; (Constructor;
- [Clear $proof | Try (Apply $proof;Clear $proof)])))>> ].
+Tactic Definition CoInduction proof :=
+ Cofix proof; Intros; Constructor;
+ [Clear proof | Try '(Apply proof;Clear proof)].
(* Extensional equality is an equivalence relation *)
-
Theorem EqSt_reflex : (s:Stream)(EqSt s s).
-CoInduction EqSt_reflex.
+'(CoInduction EqSt_reflex).
Reflexivity.
Qed.
Theorem sym_EqSt :
(s1:Stream)(s2:Stream)(EqSt s1 s2)->(EqSt s2 s1).
-CoInduction Eq_sym.
-(Case H;Intros;Symmetry;Assumption).
-(Case H;Intros;Assumption).
+'(CoInduction Eq_sym).
+Case H;Intros;Symmetry;Assumption.
+Case H;Intros;Assumption.
Qed.
Theorem trans_EqSt :
(s1,s2,s3:Stream)(EqSt s1 s2)->(EqSt s2 s3)->(EqSt s1 s3).
-CoInduction Eq_trans.
+'(CoInduction Eq_trans).
Transitivity (hd s2).
-(Case H; Intros; Assumption).
-(Case H0; Intros; Assumption).
+Case H; Intros; Assumption.
+Case H0; Intros; Assumption.
Apply (Eq_trans (tl s1) (tl s2) (tl s3)).
-(Case H; Trivial with datatypes).
-(Case H0; Trivial with datatypes).
+Case H; Trivial with datatypes.
+Case H0; Trivial with datatypes.
Qed.
(*
@@ -105,12 +104,12 @@ Intros m hypind.
Simpl.
Intros s1 s2 H.
Apply hypind.
-(Case H; Trivial with datatypes).
+Case H; Trivial with datatypes.
Qed.
Theorem ntheq_eqst :
(s1,s2:Stream)((n:nat)(Str_nth n s1)=(Str_nth n s2))->(EqSt s1 s2).
-CoInduction Equiv2.
+'(CoInduction Equiv2).
Apply (H O).
Intros n; Apply (H (S n)).
Qed.
@@ -139,7 +138,7 @@ Hypothesis InvThenP : (x:Stream)(Inv x)->(P x).
Hypothesis InvIsStable: (x:Stream)(Inv x)->(Inv (tl x)).
Theorem ForAll_coind : (x:Stream)(Inv x)->(ForAll x).
-CoInduction ForAll_coind;Auto.
+'(CoInduction ForAll_coind);Auto.
Qed.
End Co_Induction_ForAll.