update in ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / rtmap_sle.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sle.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sle.ma
index cebc3aa4a463d03f786933939c3d890999c25f43..fb59fcb786e84c360886d3642fdf2843e9ae6660 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sle.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_sle.ma
@@ -24,16 +24,30 @@ coinductive sle: relation rtmap ≝
 .
 
 interpretation "inclusion (rtmap)"
-   'subseteq t1 t2 = (sle t1 t2).
+   'subseteq f1 f2 = (sle f1 f2).
 
 (* Basic properties *********************************************************)
 
-corec lemma sle_refl: ∀f1,f2. f1 ≗ f2 → f1 ⊆ f2.
-#f1 #f2 * -f1 -f2
-#f1 #f2 #g1 #g2 #H12 #H1 #H2
-[ @(sle_push … H1 H2) | @(sle_next … H1 H2) ] -H1 -H2 /2 width=1 by/
+axiom sle_eq_repl_back1: ∀f2. eq_repl_back … (λf1. f1 ⊆ f2).
+
+lemma sle_eq_repl_fwd1: ∀f2. eq_repl_fwd … (λf1. f1 ⊆ f2).
+#f2 @eq_repl_sym /2 width=3 by sle_eq_repl_back1/
+qed-.
+
+axiom sle_eq_repl_back2: ∀f1. eq_repl_back … (λf2. f1 ⊆ f2).
+
+lemma sle_eq_repl_fwd2: ∀f1. eq_repl_fwd … (λf2. f1 ⊆ f2).
+#f1 @eq_repl_sym /2 width=3 by sle_eq_repl_back2/
+qed-.
+
+corec lemma sle_refl: ∀f. f ⊆ f.
+#f cases (pn_split f) * #g #H
+[ @(sle_push … H H) | @(sle_next … H H) ] -H //
 qed.
 
+lemma sle_refl_eq: ∀f1,f2. f1 ≗ f2 → f1 ⊆ f2.
+/2 width=3 by sle_eq_repl_back2/ qed.
+
 (* Basic inversion lemmas ***************************************************)
 
 lemma sle_inv_xp: ∀g1,g2. g1 ⊆ g2 → ∀f2. ↑f2 = g2 →
@@ -69,7 +83,7 @@ lemma sle_inv_pp: ∀g1,g2. g1 ⊆ g2 → ∀f1,f2. ↑f1 = g1 → ↑f2 = g2 
 #x1 #H #Hx1 destruct lapply (injective_push … Hx1) -Hx1 //
 qed-.
 
-lemma sle_inv_nn: ∀g1,g2. g1 ⊆ g2 → ∀f1,f2.  ⫯f1 = g1 → ⫯f2 = g2 → f1 ⊆ f2.
+lemma sle_inv_nn: ∀g1,g2. g1 ⊆ g2 → ∀f1,f2. ⫯f1 = g1 → ⫯f2 = g2 → f1 ⊆ f2.
 #g1 #g2 #H #f1 #f2 #H1 #H2 elim (sle_inv_nx … H … H1) -g1
 #x2 #H #Hx2 destruct lapply (injective_next … Hx2) -Hx2 //
 qed-.
@@ -132,6 +146,12 @@ lemma sle_inv_tl_dx: ∀f1,f2. f1 ⊆ ⫱f2 → ↑f1 ⊆ f2.
 /2 width=5 by sle_push, sle_weak/
 qed-.
 
+(* Properties with iteraded tail ********************************************)
+
+lemma sle_tls: ∀f1,f2. f1 ⊆ f2 → ∀i. ⫱*[i] f1 ⊆ ⫱*[i] f2.
+#f1 #f2 #Hf12 #i elim i -i /2 width=5 by sle_tl/
+qed.
+
 (* Properties with isid *****************************************************)
 
 corec lemma sle_isid_sn: ∀f1. 𝐈⦃f1⦄ → ∀f2. f1 ⊆ f2.