diff options
Diffstat (limited to 'theories/Wellfounded/Inverse_Image.v')
| -rw-r--r-- | theories/Wellfounded/Inverse_Image.v | 16 |
1 files changed, 8 insertions, 8 deletions
diff --git a/theories/Wellfounded/Inverse_Image.v b/theories/Wellfounded/Inverse_Image.v index 9afffc95c..ac828ac1a 100644 --- a/theories/Wellfounded/Inverse_Image.v +++ b/theories/Wellfounded/Inverse_Image.v @@ -19,10 +19,10 @@ Section Inverse_Image. Local Rof : A->A->Prop := [x,y:A](R (f x) (f y)). Remark Acc_lemma : (y:B)(Acc B R y)->(x:A)(y=(f x))->(Acc A Rof x). - Induction 1; Intros. - Apply Acc_intro; Intros. - Apply (H1 (f y0)); Try Trivial. - Rewrite H2; Trivial. + NewInduction 1 as [y _ IHAcc]; Intros x H. + Apply Acc_intro; Intros y0 H1. + Apply (IHAcc (f y0)); Try Trivial. + Rewrite H; Trivial. Qed. Lemma Acc_inverse_image : (x:A)(Acc B R (f x)) -> (Acc A Rof x). @@ -39,10 +39,10 @@ Section Inverse_Image. Lemma Acc_inverse_rel : (b:B)(Acc B R b)->(x:A)(F x b)->(Acc A RoF x). -Induction 1; Intros. -Constructor; Intros. -Case H3; Intros. -Apply (H1 x1); Auto. +NewInduction 1 as [x _ IHAcc]; Intros x0 H2. +Constructor; Intros y H3. +NewDestruct H3. +Apply (IHAcc x1); Auto. Save. |