diff options
| -rwxr-xr-x | theories/Arith/Mult.v | 11 | ||||
| -rw-r--r-- | theories/ZArith/fast_integer.v | 11 |
2 files changed, 11 insertions, 11 deletions
diff --git a/theories/Arith/Mult.v b/theories/Arith/Mult.v index 761979db3f..14dd98dacb 100755 --- a/theories/Arith/Mult.v +++ b/theories/Arith/Mult.v @@ -129,6 +129,17 @@ 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. diff --git a/theories/ZArith/fast_integer.v b/theories/ZArith/fast_integer.v index cb33104e41..4026ba2229 100644 --- a/theories/ZArith/fast_integer.v +++ b/theories/ZArith/fast_integer.v @@ -1095,17 +1095,6 @@ Do 2 Rewrite convert_add; Do 2 Rewrite times_convert; Do 3 Rewrite (mult_sym (convert x)); Apply mult_plus_distr. 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. - Theorem times_true_sub_distr: (x,y,z:positive) (compare y z EGAL) = SUPERIEUR -> (times x (true_sub y z)) = (true_sub (times x y) (times x z)). |