we removed about 100 match-with costruction turning them into applications

[helm.git] / helm / software / matita / contribs / RELATIONAL / NLE / props.ma

diff --git a/helm/software/matita/contribs/RELATIONAL/NLE/props.ma b/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
index e961f5a9ced40c39a053ab7d7d07f88455a91bc8..066e056e0435f74c01f0dc43970bbce5a2575994 100644 (file)
--- a/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NLE/props.ma
@@ -17,22 +17,20 @@ set "baseuri" "cic:/matita/RELATIONAL/NLE/props".
 include "NLE/fwd.ma".
 
 theorem nle_refl: \forall x. x <= x.
- intros 1; elim x; clear x; intros; auto.
+ intros 1; elim x; clear x; intros; auto new.
 qed.
 
 theorem nle_trans_succ: \forall x,y. x <= y \to x <= succ y.
- intros. elim H; clear H x y; intros; auto.
+ intros. elim H; clear H x y; intros; auto new.
 qed.
 
 theorem nle_lt_or_eq: \forall y,x. x <= y \to x < y \lor x = y.
  intros 1. elim y; clear y; intros;
- [ lapply linear nle_gen_zero_2 to H. auto
+ [ lapply linear nle_gen_zero_2 to H. auto new
  | lapply linear nle_gen_succ_2 to H1. decompose;
-   [ rewrite > H1. clear H1. auto
+   [ subst. auto new
    | lapply linear H to H3 as H0. decompose;
-     [ rewrite > H1. clear H1 x. auto
-     | rewrite < H. clear H n. auto
-     ]
+     subst; auto new
    ]
  ].
 qed.