auto => auto new

[helm.git] / matita / contribs / RELATIONAL / NLE / fwd.ma

diff --git a/matita/contribs/RELATIONAL/NLE/fwd.ma b/matita/contribs/RELATIONAL/NLE/fwd.ma
index dd0a7cea6a958fb9af6de022a7f9a7d5eabedf24..7d8a9e3b3528b127769d3d9e130401baf3453554 100644 (file)
--- a/matita/contribs/RELATIONAL/NLE/fwd.ma
+++ b/matita/contribs/RELATIONAL/NLE/fwd.ma
@@ -20,12 +20,12 @@ include "Nat/fwd.ma".
 include "NLE/defs.ma".
 
 theorem nle_gen_succ_1: \forall x,y. x < y \to 
-                         \exists z. y = succ z \land x <= z.
+                        \exists z. y = succ z \land x <= z.
  intros. inversion H; clear H; intros;
  [ apply (eq_gen_succ_zero ? ? H)
  | lapply linear eq_gen_succ_succ to H2 as H0.
-   rewrite > H0. clear H0.
-   apply ex_intro; [|auto] (**)
+   subst.
+   apply ex_intro; [|auto new] (**)
  ].
 qed.
 
@@ -34,8 +34,7 @@ theorem nle_gen_succ_succ: \forall x,y. x < succ y \to x <= y.
  [ apply (eq_gen_succ_zero ? ? H)
  | lapply linear eq_gen_succ_succ to H2 as H0.
    lapply linear eq_gen_succ_succ to H3 as H2.
-   rewrite > H0. rewrite > H2. clear H0 H2.
-   auto
+   subst. auto new
  ].
 qed.
 
@@ -47,16 +46,16 @@ qed.
 
 theorem nle_gen_zero_2: \forall x. x <= zero \to x = zero.
  intros 1. elim x; clear x; intros;
- [ auto
+ [ auto new
  | apply (nle_gen_succ_zero ? ? H1)
  ].
 qed.
 
 theorem nle_gen_succ_2: \forall y,x. x <= succ y \to
-                         x = zero \lor \exists z. x = succ z \land z <= y.
+                        x = zero \lor \exists z. x = succ z \land z <= y.
  intros 2; elim x; clear x; intros;
- [ auto
+ [ auto new
  | lapply linear nle_gen_succ_succ to H1.
-   right. apply ex_intro; [|auto] (**)
+   right. apply ex_intro; [|auto new] (**)
  ].
 qed.