diff options
author | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-11-05 13:44:21 +0000 |
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committer | herbelin <herbelin@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-11-05 13:44:21 +0000 |
commit | bd981e0dc87900ad7f180b4c4044fc6858d2b40a (patch) | |
tree | be811db066735fd2bd96fd7c23ba820446d6097a /theories/Arith/Mult.v | |
parent | e9bcc972d8acdf7fc83bd83e1a98af0e50390b6c (diff) |
Redondances
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@4806 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Arith/Mult.v')
-rwxr-xr-x | theories/Arith/Mult.v | 17 |
1 files changed, 6 insertions, 11 deletions
diff --git a/theories/Arith/Mult.v b/theories/Arith/Mult.v index 99dc47942..f56ee2f60 100755 --- a/theories/Arith/Mult.v +++ b/theories/Arith/Mult.v @@ -127,6 +127,12 @@ Proof. Qed. Hints Resolve mult_lt : arith. +V7only [ +Notation lt_mult_left := mult_lt. +(* Theorem lt_mult_left : + (x,y,z:nat) (lt x y) -> (lt (mult (S z) x) (mult (S z) y)). +*) +]. Lemma lt_mult_right : (m,n,p:nat) (lt m n) -> (lt (0) p) -> (lt (mult m p) (mult n p)). @@ -137,17 +143,6 @@ Rewrite mult_sym. Replace (mult n (S p)) with (mult (S p) n); Auto with arith. Qed. -Theorem lt_mult_left : - (x,y,z:nat) (lt x y) -> (lt (mult (S z) x) (mult (S z) y)). -Proof. -Intros x y z H;Elim z; [ - Simpl; Do 2 Rewrite <- plus_n_O; Assumption -| Simpl; Intros n H1; Apply lt_trans with m:=(plus y (plus x (mult n x))); [ - Rewrite (plus_sym x (plus x (mult n x))); - Rewrite (plus_sym y (plus x (mult n x))); Apply lt_reg_l; Assumption - | Apply lt_reg_l;Assumption ]]. -Qed. - Lemma mult_le_conv_1 : (m,n,p:nat) (le (mult (S m) n) (mult (S m) p)) -> (le n p). Proof. Intros. Elim (le_or_lt n p). Trivial. |