- renamed ocaml/ to components/

[helm.git] / helm / matita / library / nat / plus.ma

diff --git a/helm/matita/library/nat/plus.ma b/helm/matita/library/nat/plus.ma
deleted file mode 100644 (file)
index d595dad..0000000
--- a/helm/matita/library/nat/plus.ma
+++ /dev/null
@@ -1,72 +0,0 @@
-(**************************************************************************)
-(*       ___                                                               *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||       A.Asperti, C.Sacerdoti Coen,                          *)
-(*      ||A||       E.Tassi, S.Zacchiroli                                 *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU Lesser General Public License Version 2.1         *)
-(*                                                                        *)
-(**************************************************************************)
-
-set "baseuri" "cic:/matita/nat/plus".
-
-include "nat/nat.ma".
-
-let rec plus n m \def 
- match n with 
- [ O \Rightarrow m
- | (S p) \Rightarrow S (plus p m) ].
-
-(*CSC: the URI must disappear: there is a bug now *)
-interpretation "natural plus" 'plus x y = (cic:/matita/nat/plus/plus.con x y).
-
-theorem plus_n_O: \forall n:nat. n = n+O.
-intros.elim n.
-simplify.reflexivity.
-simplify.apply eq_f.assumption.
-qed.
-
-theorem plus_n_Sm : \forall n,m:nat. S (n+m) = n+(S m).
-intros.elim n.
-simplify.reflexivity.
-simplify.apply eq_f.assumption.
-qed.
-
-theorem sym_plus: \forall n,m:nat. n+m = m+n.
-intros.elim n.
-simplify.apply plus_n_O.
-simplify.rewrite > H.apply plus_n_Sm.
-qed.
-
-theorem associative_plus : associative nat plus.
-unfold associative.intros.elim x.
-simplify.reflexivity.
-simplify.apply eq_f.assumption.
-qed.
-
-theorem assoc_plus : \forall n,m,p:nat. (n+m)+p = n+(m+p)
-\def associative_plus.
-
-theorem injective_plus_r: \forall n:nat.injective nat nat (\lambda m.n+m).
-intro.simplify.intros 2.elim n.
-exact H.
-apply H.apply inj_S.apply H1.
-qed.
-
-theorem inj_plus_r: \forall p,n,m:nat. p+n = p+m \to n=m
-\def injective_plus_r.
-
-theorem injective_plus_l: \forall m:nat.injective nat nat (\lambda n.n+m).
-intro.simplify.intros.
-apply (injective_plus_r m).
-rewrite < sym_plus.
-rewrite < (sym_plus y).
-assumption.
-qed.
-
-theorem inj_plus_l: \forall p,n,m:nat. n+p = m+p \to n=m
-\def injective_plus_l.