some improvements

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

diff --git a/helm/software/matita/contribs/RELATIONAL/NLE/fwd.ma b/helm/software/matita/contribs/RELATIONAL/NLE/fwd.ma
index afefbfd4db919ed53eea720b2dc927d4047555e0..06b7c6fefbba15e75e0c043e73c98c2df18ac769 100644 (file)
--- a/helm/software/matita/contribs/RELATIONAL/NLE/fwd.ma
+++ b/helm/software/matita/contribs/RELATIONAL/NLE/fwd.ma
@@ -16,44 +16,41 @@ set "baseuri" "cic:/matita/RELATIONAL/NLE/fwd".
 
 include "logic/connectives.ma".
 
-include "NPlus/fwd.ma". 
+include "NPlus/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.
- unfold NLE. 
- intros. decompose.
- lapply linear nplus_gen_succ_2 to H1 as H.
- decompose. subst.
- apply ex_intro;[| auto] (**)
+theorem nle_inv_succ_1: \forall x,y. x < y \to 
+                         \exists z. y = succ z \land x <= z.
+ intros. elim H.
+ lapply linear nplus_gen_succ_2 to H1.
+ decompose. subst. auto depth = 4.
 qed.
 
-
-theorem nle_gen_succ_succ: \forall x,y. x < succ y \to x <= y.
+theorem nle_inv_succ_succ: \forall x,y. x < succ y \to x <= y.
  intros.
- lapply linear nle_gen_succ_1 to H as H0. decompose H0.
- lapply linear eq_gen_succ_succ to H1 as H. subst.
+ lapply linear nle_inv_succ_1 to H. decompose.
+ lapply linear eq_gen_succ_succ to H1. subst.
  auto.
 qed.
 
-theorem nle_gen_succ_zero: \forall x. x < zero \to False.
+theorem nle_inv_succ_zero: \forall x. x < zero \to False.
  intros.
- lapply linear nle_gen_succ_1 to H. decompose.
+ lapply linear nle_inv_succ_1 to H. decompose.
  lapply linear eq_gen_zero_succ to H1. decompose.
 qed.
 
-theorem nle_gen_zero_2: \forall x. x <= zero \to x = zero.
+theorem nle_inv_zero_2: \forall x. x <= zero \to x = zero.
  intros 1. elim x; clear x; intros;
- [ auto new timeout=30
- | lapply linear nle_gen_succ_zero to H1. decompose.
+ [ auto
+ | lapply linear nle_inv_succ_zero to H1. decompose.
  ].
 qed.
 
-theorem nle_gen_succ_2: \forall y,x. x <= succ y \to
+theorem nle_inv_succ_2: \forall y,x. x <= succ y \to
                         x = zero \lor \exists z. x = succ z \land z <= y.
  intros 2; elim x; clear x; intros;
- [ auto new timeout=30
- | lapply linear nle_gen_succ_succ to H1.
-   right. apply ex_intro; [|auto new timeout=30] (**)
+ [ auto
+ | lapply linear nle_inv_succ_succ to H1.
+   auto depth = 4.
  ].
 qed.