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authorGravatar notin <notin@85f007b7-540e-0410-9357-904b9bb8a0f7>2006-10-17 12:53:34 +0000
committerGravatar notin <notin@85f007b7-540e-0410-9357-904b9bb8a0f7>2006-10-17 12:53:34 +0000
commit28dc7a05cc1d3e03ed1435b3db4340db954a59e2 (patch)
tree63cdf18cd47260eb90550f62f7b22e2e2e208f6c /theories/Wellfounded/Disjoint_Union.v
parent744e7f6a319f4d459a3cc2309f575d43041d75aa (diff)
Mise en forme des theories
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@9245 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Wellfounded/Disjoint_Union.v')
-rw-r--r--theories/Wellfounded/Disjoint_Union.v72
1 files changed, 36 insertions, 36 deletions
diff --git a/theories/Wellfounded/Disjoint_Union.v b/theories/Wellfounded/Disjoint_Union.v
index 76c9ad443..c82549e37 100644
--- a/theories/Wellfounded/Disjoint_Union.v
+++ b/theories/Wellfounded/Disjoint_Union.v
@@ -15,41 +15,41 @@
Require Import Relation_Operators.
Section Wf_Disjoint_Union.
-Variables A B : Set.
-Variable leA : A -> A -> Prop.
-Variable leB : B -> B -> Prop.
-
-Notation Le_AsB := (le_AsB A B leA leB).
-
-Lemma acc_A_sum : forall x:A, Acc leA x -> Acc Le_AsB (inl B x).
-Proof.
- induction 1.
- apply Acc_intro; intros y H2.
- inversion_clear H2.
- auto with sets.
-Qed.
-
-Lemma acc_B_sum :
- well_founded leA -> forall x:B, Acc leB x -> Acc Le_AsB (inr A x).
-Proof.
- induction 2.
- apply Acc_intro; intros y H3.
- inversion_clear H3; auto with sets.
- apply acc_A_sum; auto with sets.
-Qed.
-
-
-Lemma wf_disjoint_sum :
- well_founded leA -> well_founded leB -> well_founded Le_AsB.
-Proof.
- intros.
- unfold well_founded in |- *.
- destruct a as [a| b].
- apply (acc_A_sum a).
- apply (H a).
-
- apply (acc_B_sum H b).
- apply (H0 b).
-Qed.
+ Variables A B : Set.
+ Variable leA : A -> A -> Prop.
+ Variable leB : B -> B -> Prop.
+
+ Notation Le_AsB := (le_AsB A B leA leB).
+
+ Lemma acc_A_sum : forall x:A, Acc leA x -> Acc Le_AsB (inl B x).
+ Proof.
+ induction 1.
+ apply Acc_intro; intros y H2.
+ inversion_clear H2.
+ auto with sets.
+ Qed.
+
+ Lemma acc_B_sum :
+ well_founded leA -> forall x:B, Acc leB x -> Acc Le_AsB (inr A x).
+ Proof.
+ induction 2.
+ apply Acc_intro; intros y H3.
+ inversion_clear H3; auto with sets.
+ apply acc_A_sum; auto with sets.
+ Qed.
+
+
+ Lemma wf_disjoint_sum :
+ well_founded leA -> well_founded leB -> well_founded Le_AsB.
+ Proof.
+ intros.
+ unfold well_founded in |- *.
+ destruct a as [a| b].
+ apply (acc_A_sum a).
+ apply (H a).
+
+ apply (acc_B_sum H b).
+ apply (H0 b).
+ Qed.
End Wf_Disjoint_Union. \ No newline at end of file