diff options
author | notin <notin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2006-10-17 12:53:34 +0000 |
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committer | notin <notin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2006-10-17 12:53:34 +0000 |
commit | 28dc7a05cc1d3e03ed1435b3db4340db954a59e2 (patch) | |
tree | 63cdf18cd47260eb90550f62f7b22e2e2e208f6c /theories/Wellfounded/Disjoint_Union.v | |
parent | 744e7f6a319f4d459a3cc2309f575d43041d75aa (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.v | 72 |
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.
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