X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_transition%2Flpr.ma;h=646689287619ce00a727a8250c26207b40fcce7f;hb=bd53c4e895203eb049e75434f638f26b5a161a2b;hp=f644a728ffa6b85eb2b7f490922e684f8478207c;hpb=e9f96fa56226dfd74de214c89d827de0c5018ac7;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
index f644a728f..646689287 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
@@ -12,49 +12,86 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predsn_3.ma".
-include "basic_2/substitution/lpx_sn.ma".
-include "basic_2/reduction/cpr.ma".
+include "basic_2/notation/relations/predsn_4.ma".
+include "static_2/relocation/lex.ma".
+include "basic_2/rt_transition/cpr_ext.ma".
 
-(* SN PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS *****************************)
+(* PARALLEL R-TRANSITION FOR FULL LOCAL ENVIRONMENTS ************************)
 
-definition lpr: relation3 genv lenv lenv ≝ λG. lpx_sn (cpr G).
+definition lpr (h) (G): relation lenv ≝
+                        lex (λL. cpm h G L 0).
 
-interpretation "parallel reduction (local environment, sn variant)"
-   'PRedSn G L1 L2 = (lpr G L1 L2).
+interpretation
+   "parallel rt-transition (full local environment)"
+   'PRedSn h G L1 L2 = (lpr h G L1 L2).
+
+(* Basic properties *********************************************************)
+
+lemma lpr_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.
+
+(* Note: lemma 250 *)
+lemma lpr_refl (h) (G): reflexive … (lpr h G).
+/2 width=1 by lex_refl/ qed.
+
+(* Advanced properties ******************************************************)
+
+lemma lpr_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 lpr_pair (h) (G): ∀K1,K2,V1,V2. ❪G,K1❫ ⊢ ➡[h] K2 → ❪G,K1❫ ⊢ V1 ➡[h] V2 →
+                        ∀I. ❪G,K1.ⓑ[I]V1❫ ⊢ ➡[h] K2.ⓑ[I]V2.
+/2 width=1 by lex_pair/ qed.
 
 (* Basic inversion lemmas ***************************************************)
 
+(* Basic_2A1: was: lpr_inv_atom1 *)
 (* Basic_1: includes: wcpr0_gen_sort *)
-lemma lpr_inv_atom1: ∀G,L2. ⦃G, ⋆⦄ ⊢ ➡ L2 → L2 = ⋆.
-/2 width=4 by lpx_sn_inv_atom1_aux/ qed-.
+lemma lpr_inv_atom_sn (h) (G): ∀L2. ❪G,⋆❫ ⊢ ➡[h] L2 → L2 = ⋆.
+/2 width=2 by lex_inv_atom_sn/ qed-.
 
-(* Basic_1: includes: wcpr0_gen_head *)
-lemma lpr_inv_pair1: ∀I,G,K1,V1,L2. ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ L2 →
-                     ∃∃K2,V2. ⦃G, K1⦄ ⊢ ➡ K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2 & L2 = K2.ⓑ{I}V2.
-/2 width=3 by lpx_sn_inv_pair1_aux/ qed-.
+lemma lpr_inv_bind_sn (h) (G): ∀I1,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-.
 
-lemma lpr_inv_atom2: ∀G,L1. ⦃G, L1⦄ ⊢ ➡ ⋆ → L1 = ⋆.
-/2 width=4 by lpx_sn_inv_atom2_aux/ qed-.
+(* Basic_2A1: was: lpr_inv_atom2 *)
+lemma lpr_inv_atom_dx (h) (G): ∀L1. ❪G,L1❫ ⊢ ➡[h] ⋆ → L1 = ⋆.
+/2 width=2 by lex_inv_atom_dx/ qed-.
 
-lemma lpr_inv_pair2: ∀I,G,L1,K2,V2. ⦃G, L1⦄ ⊢ ➡ K2.ⓑ{I}V2 →
-                     ∃∃K1,V1. ⦃G, K1⦄ ⊢ ➡ K2 & ⦃G, K1⦄ ⊢ V1 ➡ V2 & L1 = K1. ⓑ{I} V1.
-/2 width=3 by lpx_sn_inv_pair2_aux/ qed-.
+lemma lpr_inv_bind_dx (h) (G): ∀I2,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-.
 
-(* Basic properties *********************************************************)
+(* Advanced inversion lemmas ************************************************)
 
-(* Note: lemma 250 *)
-lemma lpr_refl: ∀G,L. ⦃G, L⦄ ⊢ ➡ L.
-/2 width=1 by lpx_sn_refl/ qed.
+lemma lpr_inv_unit_sn (h) (G): ∀I,L2,K1. ❪G,K1.ⓤ[I]❫ ⊢ ➡[h] L2 →
+                               ∃∃K2. ❪G,K1❫ ⊢ ➡[h] K2 & L2 = K2.ⓤ[I].
+/2 width=1 by lex_inv_unit_sn/ qed-.
+
+(* Basic_2A1: was: lpr_inv_pair1 *)
+(* Basic_1: includes: wcpr0_gen_head *)
+lemma lpr_inv_pair_sn (h) (G): ∀I,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 lpr_pair: ∀I,G,K1,K2,V1,V2. ⦃G, K1⦄ ⊢ ➡ K2 → ⦃G, K1⦄ ⊢ V1 ➡ V2 →
-                ⦃G, K1.ⓑ{I}V1⦄ ⊢ ➡ K2.ⓑ{I}V2.
-/2 width=1 by lpx_sn_pair/ qed.
+lemma lpr_inv_unit_dx (h) (G): ∀I,L1,K2. ❪G,L1❫ ⊢ ➡[h] K2.ⓤ[I] →
+                               ∃∃K1. ❪G,K1❫ ⊢ ➡[h] K2 & L1 = K1.ⓤ[I].
+/2 width=1 by lex_inv_unit_dx/ qed-.
 
-(* Basic forward lemmas *****************************************************)
+(* Basic_2A1: was: lpr_inv_pair2 *)
+lemma lpr_inv_pair_dx (h) (G): ∀I,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-.
 
-lemma lpr_fwd_length: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → |L1| = |L2|.
-/2 width=2 by lpx_sn_fwd_length/ qed-.
+lemma lpr_inv_pair (h) (G): ∀I1,I2,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-.
 
 (* Basic_1: removed theorems 3: wcpr0_getl wcpr0_getl_back
                                 pr0_subst1_back