- equivalence between lfpxs and lpxs + lfeq proved

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / lpx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
index cde540dcc53c6f148cb3189e5ecc1baa932c2a47..a5d9966beeb46a15e503b920e970bbc27b690426 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
@@ -14,7 +14,7 @@
 
 include "basic_2/notation/relations/predtysn_4.ma".
 include "basic_2/relocation/lex.ma".
-include "basic_2/rt_transition/cpx.ma".
+include "basic_2/rt_transition/cpx_ext.ma".
 
 (* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENVIRONMENTS ******************)
 
@@ -27,39 +27,57 @@ interpretation
 
 (* Basic properties *********************************************************)
 
+lemma lpx_bind: ∀h,G,K1,K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 →
+                ∀I1,I2. ⦃G, K1⦄ ⊢ I1 ⬈[h] I2 → ⦃G, K1.ⓘ{I1}⦄ ⊢ ⬈[h] K2.ⓘ{I2}.
+/2 width=1 by lex_bind/ qed.
+
+lemma lpx_refl: ∀h,G. reflexive … (lpx h G).
+/2 width=1 by lex_refl/ qed.
+
+(* Advanced properties ******************************************************)
+
+lemma lpx_bind_refl_dx: ∀h,G,K1,K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 →
+                        ∀I. ⦃G, K1.ⓘ{I}⦄ ⊢ ⬈[h] K2.ⓘ{I}.
+/2 width=1 by lex_bind_refl_dx/ qed.
 (*
 lemma lpx_pair: ∀h,g,I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ⬈[h] K2 → ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 →
                 ⦃G, K1.ⓑ{I}V1⦄ ⊢ ⬈[h] K2.ⓑ{I}V2.
 /2 width=1 by lpx_sn_pair/ qed.
 *)
-
-lemma lpx_refl: ∀h,G. reflexive … (lpx h G).
-/2 width=1 by lex_refl/ qed.
-
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: was: lpx_inv_atom1 *)
 lemma lpx_inv_atom_sn: ∀h,G,L2. ⦃G, ⋆⦄ ⊢ ⬈[h] L2 → L2 = ⋆.
 /2 width=2 by lex_inv_atom_sn/ qed-.
 
+lemma lpx_inv_bind_sn: ∀h,I1,G,L2,K1. ⦃G, K1.ⓘ{I1}⦄ ⊢ ⬈[h] L2 →
+                       ∃∃I2,K2. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ I1 ⬈[h] I2 &
+                                L2 = K2.ⓘ{I2}.
+/2 width=1 by lex_inv_bind_sn/ qed-.
+
+(* Basic_2A1: was: lpx_inv_atom2 *)
+lemma lpx_inv_atom_dx: ∀h,G,L1.  ⦃G, L1⦄ ⊢ ⬈[h] ⋆ → L1 = ⋆.
+/2 width=2 by lex_inv_atom_dx/ qed-.
+
+lemma lpx_inv_bind_dx: ∀h,I2,G,L1,K2.  ⦃G, L1⦄ ⊢ ⬈[h] K2.ⓘ{I2} →
+                       ∃∃I1,K1. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ I1 ⬈[h] I2 &
+                                L1 = K1.ⓘ{I1}.
+/2 width=1 by lex_inv_bind_dx/ qed-.
+
+(* Advanced inversion lemmas ************************************************)
+
 (* Basic_2A1: was: lpx_inv_pair1 *)
 lemma lpx_inv_pair_sn: ∀h,I,G,L2,K1,V1. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ⬈[h] L2 →
                        ∃∃K2,V2. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 &
                                 L2 = K2.ⓑ{I}V2.
 /2 width=1 by lex_inv_pair_sn/ qed-.
 
-(* Basic_2A1: was: lpx_inv_atom2 *)
-lemma lpx_inv_atom_dx: ∀h,G,L1.  ⦃G, L1⦄ ⊢ ⬈[h] ⋆ → L1 = ⋆.
-/2 width=2 by lex_inv_atom_dx/ qed-.
-
 (* Basic_2A1: was: lpx_inv_pair2 *)
-lemma lpx_inv_pair2_dx: ∀h,I,G,L1,K2,V2.  ⦃G, L1⦄ ⊢ ⬈[h] K2.ⓑ{I}V2 →
-                        ∃∃K1,V1. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 &
-                                 L1 = K1.ⓑ{I}V1.
+lemma lpx_inv_pair_dx: ∀h,I,G,L1,K2,V2.  ⦃G, L1⦄ ⊢ ⬈[h] K2.ⓑ{I}V2 →
+                       ∃∃K1,V1. ⦃G, K1⦄ ⊢ ⬈[h] K2 & ⦃G, K1⦄ ⊢ V1 ⬈[h] V2 &
+                                L1 = K1.ⓑ{I}V1.
 /2 width=1 by lex_inv_pair_dx/ qed-.
 
-(* Advanced inversion lemmas ************************************************)
-
 lemma lpx_inv_pair: ∀h,I1,I2,G,L1,L2,V1,V2.  ⦃G, L1.ⓑ{I1}V1⦄ ⊢ ⬈[h] L2.ⓑ{I2}V2 →
                     ∧∧ ⦃G, L1⦄ ⊢ ⬈[h] L2 & ⦃G, L1⦄ ⊢ V1 ⬈[h] V2 & I1 = I2.
 /2 width=1 by lex_inv_pair/ qed-.