patched

[helm.git] / matita / contribs / RELATIONAL-ARITHMETICS / add_props.ma

diff --git a/matita/contribs/RELATIONAL-ARITHMETICS/add_props.ma b/matita/contribs/RELATIONAL-ARITHMETICS/add_props.ma
index 86aa7c1925b1ee6b1e4bd51480ad114fa5816800..6d2bef8232e910d91938fdea03fcde7d37812a3f 100644 (file)
--- a/matita/contribs/RELATIONAL-ARITHMETICS/add_props.ma
+++ b/matita/contribs/RELATIONAL-ARITHMETICS/add_props.ma
@@ -14,26 +14,8 @@
 
 set "baseuri" "cic:/matita/RELATIONAL-ARITHMETICS/add_props".
 
-include "nat_props.ma".
-include "add_defs.ma".
+include "add_gen.ma".
 
-theorem add_gen_O_2: \forall p,r. add p O r \to p = r.
- intros. inversion H; clear H; intros;
- [ reflexivity
- | lapply eq_gen_O_S to H2 as H0. apply H0
- ].
-qed.
-
-theorem add_gen_S_2: \forall p,q,r. add p (S q) r \to 
-                     \exists s. r = (S s) \land add p q s.
- intros. inversion H; clear H; intros;
- [ lapply eq_gen_S_O to H as H0. apply H0
- | lapply eq_gen_S_S to H2 as H0. clear H2.
-   rewrite > H0. clear H0.
-   apply ex_intro; [| auto ] (**)
- ].
-qed.
-  
 theorem add_O_1: \forall q. add O q q.
  intros. elim q; clear q; auto.
 qed.
@@ -66,15 +48,6 @@ theorem add_shift_S_sx: \forall p,q,r. add p (S q) r \to add (S p) q r.
  auto.
 qed.
 
-theorem add_gen_O_1: \forall q,r. add O q r \to q = r.
- intros. auto.
-qed.
-
-theorem add_gen_S_1: \forall p,q,r. add (S p) q r \to 
-                     \exists s. r = (S s) \land add p q s.
- intros. auto.
-qed.
-
 theorem add_shift_S_dx: \forall p,q,r. add (S p) q r \to add p (S q) r.
  intros.
  lapply add_gen_S_1 to H as H0. clear H.