- lpx and lpxs restored to prove equivalene between lfpxs and lpxs + lfeq

[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 bd4e16df9444deb3064a9c9a2972bb1ccbd525bf..cde540dcc53c6f148cb3189e5ecc1baa932c2a47 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
@@ -12,54 +12,54 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predsn_5.ma".
-include "basic_2/reduction/lpr.ma".
-include "basic_2/reduction/cpx.ma".
+include "basic_2/notation/relations/predtysn_4.ma".
+include "basic_2/relocation/lex.ma".
+include "basic_2/rt_transition/cpx.ma".
 
-(* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
+(* UNCOUNTED PARALLEL RT-TRANSITION FOR LOCAL ENVIRONMENTS ******************)
 
-definition lpx: ∀h. sd h → relation3 genv lenv lenv ≝
-                λh,o,G. lpx_sn (cpx h o G).
+definition lpx: sh → genv → relation lenv ≝
+                λh,G. lex (cpx h G).
 
-interpretation "extended parallel reduction (local environment, sn variant)"
-   'PRedSn h o G L1 L2 = (lpx h o G L1 L2).
+interpretation
+   "uncounted parallel rt-transition (local environment)"
+   'PRedTySn h G L1 L2 = (lpx h G L1 L2).
 
-(* Basic inversion lemmas ***************************************************)
-
-lemma lpx_inv_atom1: ∀h,o,G,L2. ⦃G, ⋆⦄ ⊢ ➡[h, o] L2 → L2 = ⋆.
-/2 width=4 by lpx_sn_inv_atom1_aux/ qed-.
-
-lemma lpx_inv_pair1: ∀h,o,I,G,K1,V1,L2. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡[h, o] L2 →
-                     ∃∃K2,V2. ⦃G, K1⦄ ⊢ ➡[h, o] K2 & ⦃G, K1⦄ ⊢ V1 ➡[h, o] V2 &
-                              L2 = K2. ⓑ{I} V2.
-/2 width=3 by lpx_sn_inv_pair1_aux/ qed-.
+(* Basic properties *********************************************************)
 
-lemma lpx_inv_atom2: ∀h,o,G,L1.  ⦃G, L1⦄ ⊢ ➡[h, o] ⋆ → L1 = ⋆.
-/2 width=4 by lpx_sn_inv_atom2_aux/ 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_inv_pair2: ∀h,o,I,G,L1,K2,V2.  ⦃G, L1⦄ ⊢ ➡[h, o] K2.ⓑ{I}V2 →
-                     ∃∃K1,V1. ⦃G, K1⦄ ⊢ ➡[h, o] K2 & ⦃G, K1⦄ ⊢ V1 ➡[h, o] V2 &
-                             L1 = K1. ⓑ{I} V1.
-/2 width=3 by lpx_sn_inv_pair2_aux/ qed-.
+lemma lpx_refl: ∀h,G. reflexive … (lpx h G).
+/2 width=1 by lex_refl/ qed.
 
-lemma lpx_inv_pair: ∀h,o,I1,I2,G,L1,L2,V1,V2.  ⦃G, L1.ⓑ{I1}V1⦄ ⊢ ➡[h, o] L2.ⓑ{I2}V2 →
-                    ∧∧ ⦃G, L1⦄ ⊢ ➡[h, o] L2 & ⦃G, L1⦄ ⊢ V1 ➡[h, o] V2 & I1 = I2.
-/2 width=1 by lpx_sn_inv_pair/ qed-.
+(* Basic inversion lemmas ***************************************************)
 
-(* Basic properties *********************************************************)
+(* 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_refl: ∀h,o,G,L.  ⦃G, L⦄ ⊢ ➡[h, o] L.
-/2 width=1 by lpx_sn_refl/ qed.
+(* 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-.
 
-lemma lpx_pair: ∀h,o,I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ➡[h, o] K2 → ⦃G, K1⦄ ⊢ V1 ➡[h, o] V2 →
-                ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡[h, o] K2.ⓑ{I}V2.
-/2 width=1 by lpx_sn_pair/ 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 lpr_lpx: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L1⦄ ⊢ ➡[h, o] L2.
-#h #o #G #L1 #L2 #H elim H -L1 -L2 /3 width=1 by lpx_pair, cpr_cpx/
-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.
+/2 width=1 by lex_inv_pair_dx/ qed-.
 
-(* Basic forward lemmas *****************************************************)
+(* Advanced inversion lemmas ************************************************)
 
-lemma lpx_fwd_length: ∀h,o,G,L1,L2. ⦃G, L1⦄ ⊢ ➡[h, o] L2 → |L1| = |L2|.
-/2 width=2 by lpx_sn_fwd_length/ qed-.
+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-.