diff options
Diffstat (limited to 'theories/Numbers/Integer/TreeMod/ZTreeMod.v')
| -rw-r--r-- | theories/Numbers/Integer/TreeMod/ZTreeMod.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/Numbers/Integer/TreeMod/ZTreeMod.v b/theories/Numbers/Integer/TreeMod/ZTreeMod.v index 75e9c9f77e..db09c2ec7a 100644 --- a/theories/Numbers/Integer/TreeMod/ZTreeMod.v +++ b/theories/Numbers/Integer/TreeMod/ZTreeMod.v @@ -212,18 +212,18 @@ rewrite Zminus_mod_idemp_l. now replace ([|n|] - ([|m|] + 1))%Z with ([|n|] - [|m|] - 1)%Z by auto with zarith. Qed. -Theorem NZtimes_0_r : forall n : NZ, n * 0 == 0. +Theorem NZtimes_0_l : forall n : NZ, 0 * n == 0. Proof. intro n; unfold NZtimes, NZ0, NZ, NZeq. rewrite w_spec.(spec_mul). -rewrite w_spec.(spec_0). now rewrite Zmult_0_r. +rewrite w_spec.(spec_0). now rewrite Zmult_0_l. Qed. -Theorem NZtimes_succ_r : forall n m : NZ, n * (S m) == n * m + n. +Theorem NZtimes_succ_l : forall n m : NZ, (S n) * m == n * m + m. Proof. intros n m; unfold NZtimes, NZsucc, NZplus, NZeq. rewrite w_spec.(spec_mul). -rewrite w_spec.(spec_add). rewrite w_spec.(spec_mul). rewrite w_spec.(spec_succ). -rewrite Zplus_mod_idemp_l. rewrite Zmult_mod_idemp_r. -rewrite Zmult_plus_distr_r. now rewrite Zmult_1_r. +rewrite w_spec.(spec_add), w_spec.(spec_mul), w_spec.(spec_succ). +rewrite Zplus_mod_idemp_l, Zmult_mod_idemp_l. +now rewrite Zmult_plus_distr_l, Zmult_1_l. Qed. End NZBigIntsAxiomsMod. |