some restyling ...

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_conversion / lpce.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/lpce.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/lpce.ma
index 8aca0e26b4b29abd55221bcf4227bcc6bf3689b9..8da6c1af49c1378e4bb34e543aff6651b478f5b9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/lpce.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_conversion/lpce.ma
@@ -14,7 +14,7 @@
 
 include "static_2/relocation/lex.ma".
 include "basic_2/notation/relations/pconveta_4.ma".
-include "basic_2/rt_conversion/cpce.ma".
+include "basic_2/rt_conversion/cpce_ext.ma".
 
 (* PARALLEL ETA-CONVERSION FOR FULL LOCAL ENVIRONMENTS **********************)
 
@@ -24,6 +24,13 @@ interpretation
   "parallel eta-conversion on all entries (local environment)"
   'PConvEta h G L1 L2 = (lpce h G L1 L2).
 
+(* Basic properties *********************************************************)
+
+lemma lpce_bind (h) (G):
+      ∀K1,K2. ⦃G,K1⦄ ⊢ ⬌η[h] K2 →
+      ∀I1,I2. ⦃G,K1⦄ ⊢ I1 ⬌η[h] I2 → ⦃G,K1.ⓘ{I1}⦄ ⊢ ⬌η[h] K2.ⓘ{I2}.
+/2 width=1 by lex_bind/ qed.
+
 (* Advanced properties ******************************************************)
 
 lemma lpce_pair (h) (G):
@@ -37,15 +44,25 @@ lemma lpce_inv_atom_sn (h) (G):
       ∀L2. ⦃G,⋆⦄ ⊢ ⬌η[h] L2 → L2 = ⋆.
 /2 width=2 by lex_inv_atom_sn/ qed-.
 
+lemma lpce_inv_bind_sn (h) (G):
+      ∀I1,L2,K1. ⦃G,K1.ⓘ{I1}⦄ ⊢ ⬌η[h] L2 →
+      ∃∃I2,K2. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & ⦃G,K1⦄ ⊢ I1 ⬌η[h] I2 & L2 = K2.ⓘ{I2}.
+/2 width=1 by lex_inv_bind_sn/ qed-.
+
 lemma lpce_inv_atom_dx (h) (G):
       ∀L1. ⦃G,L1⦄ ⊢ ⬌η[h] ⋆ → L1 = ⋆.
 /2 width=2 by lex_inv_atom_dx/ qed-.
 
+lemma lpce_inv_bind_dx (h) (G):
+      ∀I2,L1,K2. ⦃G,L1⦄ ⊢ ⬌η[h] K2.ⓘ{I2} →
+      ∃∃I1,K1. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & ⦃G,K1⦄ ⊢ I1 ⬌η[h] I2 & L1 = K1.ⓘ{I1}.
+/2 width=1 by lex_inv_bind_dx/ qed-.
+
 (* Advanced inversion lemmas ************************************************)
 
 lemma lpce_inv_unit_sn (h) (G):
       ∀I,L2,K1. ⦃G,K1.ⓤ{I}⦄ ⊢ ⬌η[h] L2 →
-      ∃∃K2. ⦃G, K1⦄ ⊢ ⬌η[h] K2 & L2 = K2.ⓤ{I}.
+      ∃∃K2. ⦃G,K1⦄ ⊢ ⬌η[h] K2 & L2 = K2.ⓤ{I}.
 /2 width=1 by lex_inv_unit_sn/ qed-.
 
 lemma lpce_inv_pair_sn (h) (G):