syntactic components detached from basic_2 become static_2

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

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 24cea1f7e910f6a123f80d0df1768e34cab9299c..f69cb5e673d3ffdbf7f325f179ff30f0dd963c49 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
@@ -12,53 +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 inversion lemmas ***************************************************)
+(* Basic properties *********************************************************)
 
-(* 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_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.
 
-(* 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-.
+(* Note: lemma 250 *)
+lemma lpr_refl (h) (G): reflexive … (lpr h G).
+/2 width=1 by lex_refl/ qed.
 
-lemma lpr_inv_atom2: ∀G,L1. ⦃G, L1⦄ ⊢ ➡ ⋆ → L1 = ⋆.
-/2 width=4 by lpx_sn_inv_atom2_aux/ qed-.
+(* Advanced properties ******************************************************)
 
-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_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.
 
-(* Basic properties *********************************************************)
+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.
 
-(* Note: lemma 250 *)
-lemma lpr_refl: ∀G,L. ⦃G, L⦄ ⊢ ➡ L.
-/2 width=1 by lpx_sn_refl/ qed.
+(* Basic inversion lemmas ***************************************************)
+
+(* Basic_2A1: was: lpr_inv_atom1 *)
+(* Basic_1: includes: wcpr0_gen_sort *)
+lemma lpr_inv_atom_sn (h) (G): ∀L2. ⦃G, ⋆⦄ ⊢ ➡[h] L2 → L2 = ⋆.
+/2 width=2 by lex_inv_atom_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_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-.
 
-(* Basic forward lemmas *****************************************************)
+(* 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_fwd_length: ∀G,L1,L2. ⦃G, L1⦄ ⊢ ➡ L2 → |L1| = |L2|.
-/2 width=2 by lpx_sn_fwd_length/ 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-.
 
-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.
+(* Advanced inversion lemmas ************************************************)
+
+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_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_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_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