X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FRELATIONAL%2FNLE%2Forder.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2FRELATIONAL%2FNLE%2Forder.ma;h=0000000000000000000000000000000000000000;hb=da0775e27b362e91ea1453a800bc403781cc2ca3;hp=473ac601d889d34fa47e01e64742d21ae1b7c3f1;hpb=d9824956d9132109ed5f23380a0a1f9c5181d18a;p=helm.git diff --git a/helm/software/matita/contribs/RELATIONAL/NLE/order.ma b/helm/software/matita/contribs/RELATIONAL/NLE/order.ma deleted file mode 100644 index 473ac601d..000000000 --- a/helm/software/matita/contribs/RELATIONAL/NLE/order.ma +++ /dev/null @@ -1,52 +0,0 @@ -(**************************************************************************) -(* ___ *) -(* ||M|| *) -(* ||A|| A project by Andrea Asperti *) -(* ||T|| *) -(* ||I|| Developers: *) -(* ||T|| The HELM team. *) -(* ||A|| http://helm.cs.unibo.it *) -(* \ / *) -(* \ / This file is distributed under the terms of the *) -(* v GNU General Public License Version 2 *) -(* *) -(**************************************************************************) - - - -include "NLE/inv.ma". - -theorem nle_refl: ∀x. x ≤ x. - intros; elim x; clear x; autobatch. -qed. - -theorem nle_trans: ∀x,y. x ≤ y → ∀z. y ≤ z → x ≤ z. - intros 3; elim H; clear H x y; - [ autobatch - | lapply linear nle_inv_succ_1 to H3. decompose. destruct. - autobatch - ]. -qed. - -theorem nle_false: ∀x,y. x ≤ y → y < x → False. - intros 3; elim H; clear H x y; autobatch. -qed. - -theorem nle_irrefl: ∀x. x < x → False. - intros. autobatch. -qed. - -theorem nle_irrefl_ei: ∀x, z. z ≤ x → z = succ x → False. - intros 3; elim H; clear H x z; destruct; autobatch. -qed. - -theorem nle_irrefl_smart: ∀x. x < x → False. - intros 1. elim x; clear x; autobatch. -qed. - -theorem nle_lt_or_eq: ∀y, x. x ≤ y → x < y ∨ x = y. - intros; elim H; clear H x y; - [ elim n; clear n - | decompose - ]; autobatch. -qed.