diff options
| -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 99dc47942b..f56ee2f60e 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. |