lemma 3.6 subverted

[helm.git] / helm / software / matita / contribs / dama / dama / supremum.ma

diff --git a/helm/software/matita/contribs/dama/dama/supremum.ma b/helm/software/matita/contribs/dama/dama/supremum.ma
index b2411f65263a318cee22f7529a0dec08baa59a60..a4df778067905ea37101fd6cde92571158343462 100644 (file)
--- a/helm/software/matita/contribs/dama/dama/supremum.ma
+++ b/helm/software/matita/contribs/dama/dama/supremum.ma
@@ -122,6 +122,17 @@ include "nat_ordered_set.ma".
 alias symbol "nleq" = "Ordered set excess".
 alias symbol "leq" = "Ordered set less or equal than".
 lemma trans_increasing: 
+  ∀C:ordered_set.∀a:sequence C.a is_increasing → ∀n,m:nat_ordered_set. n ≤ m → a n ≤ a m.
+intros 5 (C a Hs n m); elim m; [
+  rewrite > (le_n_O_to_eq n (not_lt_to_le O n H));
+  intro X; cases (os_coreflexive ?? X);]
+cases (le_to_or_lt_eq ?? (not_lt_to_le (S n1) n H1)); clear H1;
+[2: rewrite > H2; intro; cases (os_coreflexive ?? H1);
+|1: apply (le_transitive ???? (H ?) (Hs ?));
+    intro; whd in H1; apply (not_le_Sn_n n); apply (transitive_le ??? H2 H1);]
+qed.
+
+lemma trans_increasing_exc: 
   ∀C:ordered_set.∀a:sequence C.a is_increasing → ∀n,m:nat_ordered_set. m ≰ n → a n ≤ a m.
 intros 5 (C a Hs n m); elim m; [cases (not_le_Sn_O n H);]
 intro; apply H; 
@@ -153,12 +164,12 @@ lemma selection:
   ∀C:ordered_set.∀m:sequence nat_ordered_set.m is_strictly_increasing →
     ∀a:sequence C.∀u.a ↑ u → (λx.a (m x)) ↑ u.
 intros (C m Hm a u Ha); cases Ha (Ia Su); cases Su (Uu Hu); repeat split; 
-[1: intro n; simplify; apply trans_increasing; [assumption] apply (Hm n);
+[1: intro n; simplify; apply trans_increasing_exc; [assumption] apply (Hm n);
 |2: intro n; simplify; apply Uu;
 |3: intros (y Hy); simplify; cases (Hu ? Hy);
     cases (strictly_increasing_reaches C ? Hm w); 
     exists [apply w1]; cases (os_cotransitive ??? (a (m w1)) H); [2:assumption]  
-    cases (trans_increasing C ? Ia ?? H1); assumption;]
+    cases (trans_increasing_exc C ? Ia ?? H1); assumption;]
 qed.     
     
 (* Definition 2.7 *)