diff options
Diffstat (limited to 'theories/ZArith/Zminmax.v')
| -rw-r--r-- | theories/ZArith/Zminmax.v | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/theories/ZArith/Zminmax.v b/theories/ZArith/Zminmax.v index 6ea02a483..83dceb84b 100644 --- a/theories/ZArith/Zminmax.v +++ b/theories/ZArith/Zminmax.v @@ -18,32 +18,32 @@ Open Local Scope Z_scope. Lemma Zmin_max_absorption_r_r : forall n m, Zmax n (Zmin n m) = n. Proof. - intros; apply Zmin_case_strong; intro; apply Zmax_case_strong; intro; + intros; apply Zmin_case_strong; intro; apply Zmax_case_strong; intro; reflexivity || apply Zle_antisym; trivial. Qed. Lemma Zmax_min_absorption_r_r : forall n m, Zmin n (Zmax n m) = n. Proof. - intros; apply Zmax_case_strong; intro; apply Zmin_case_strong; intro; + intros; apply Zmax_case_strong; intro; apply Zmin_case_strong; intro; reflexivity || apply Zle_antisym; trivial. Qed. (** Distributivity *) -Lemma Zmax_min_distr_r : +Lemma Zmax_min_distr_r : forall n m p, Zmax n (Zmin m p) = Zmin (Zmax n m) (Zmax n p). Proof. intros. - repeat apply Zmax_case_strong; repeat apply Zmin_case_strong; intros; + repeat apply Zmax_case_strong; repeat apply Zmin_case_strong; intros; reflexivity || apply Zle_antisym; (assumption || eapply Zle_trans; eassumption). Qed. -Lemma Zmin_max_distr_r : +Lemma Zmin_max_distr_r : forall n m p, Zmin n (Zmax m p) = Zmax (Zmin n m) (Zmin n p). Proof. intros. - repeat apply Zmax_case_strong; repeat apply Zmin_case_strong; intros; + repeat apply Zmax_case_strong; repeat apply Zmin_case_strong; intros; reflexivity || apply Zle_antisym; (assumption || eapply Zle_trans; eassumption). Qed. |