update in basic_2 and apps_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 646689287619ce00a727a8250c26207b40fcce7f..2cfb7ff4de6b73f14f9c19ea4ab52d76ec60dbab 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
@@ -12,85 +12,85 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predsn_4.ma".
+include "basic_2/notation/relations/predsn_5.ma".
 include "static_2/relocation/lex.ma".
 include "basic_2/rt_transition/cpr_ext.ma".
 
 (* PARALLEL R-TRANSITION FOR FULL LOCAL ENVIRONMENTS ************************)
 
-definition lpr (h) (G): relation lenv ≝
-                        lex (λL. cpm h G L 0).
+definition lpr (h) (n) (G): relation lenv ≝
+           lex (λL. cpm h G L n).
 
 interpretation
    "parallel rt-transition (full local environment)"
-   'PRedSn h G L1 L2 = (lpr h G L1 L2).
+   'PRedSn h n G L1 L2 = (lpr h n 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].
+lemma lpr_bind (h) (G): ∀K1,K2. ❪G,K1❫ ⊢ ➡[h,0] K2 →
+                        ∀I1,I2. ❪G,K1❫ ⊢ I1 ➡[h,0] I2 → ❪G,K1.ⓘ[I1]❫ ⊢ ➡[h,0] K2.ⓘ[I2].
 /2 width=1 by lex_bind/ qed.
 
 (* Note: lemma 250 *)
-lemma lpr_refl (h) (G): reflexive … (lpr h G).
+lemma lpr_refl (h) (G): reflexive … (lpr h 0 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].
+lemma lpr_bind_refl_dx (h) (G): ∀K1,K2. ❪G,K1❫ ⊢ ➡[h,0] K2 →
+                                ∀I. ❪G,K1.ⓘ[I]❫ ⊢ ➡[h,0] 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.
+lemma lpr_pair (h) (G): ∀K1,K2,V1,V2. ❪G,K1❫ ⊢ ➡[h,0] K2 → ❪G,K1❫ ⊢ V1 ➡[h,0] V2 →
+                        ∀I. ❪G,K1.ⓑ[I]V1❫ ⊢ ➡[h,0] 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_atom_sn (h) (G): ∀L2. ❪G,⋆❫ ⊢ ➡[h] L2 → L2 = ⋆.
+lemma lpr_inv_atom_sn (h) (G): ∀L2. ❪G,⋆❫ ⊢ ➡[h,0] L2 → L2 = ⋆.
 /2 width=2 by lex_inv_atom_sn/ 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 &
+lemma lpr_inv_bind_sn (h) (G): ∀I1,L2,K1. ❪G,K1.ⓘ[I1]❫ ⊢ ➡[h,0] L2 →
+                               ∃∃I2,K2. ❪G,K1❫ ⊢ ➡[h,0] K2 & ❪G,K1❫ ⊢ I1 ➡[h,0] I2 &
                                         L2 = K2.ⓘ[I2].
 /2 width=1 by lex_inv_bind_sn/ qed-.
 
 (* Basic_2A1: was: lpr_inv_atom2 *)
-lemma lpr_inv_atom_dx (h) (G): ∀L1. ❪G,L1❫ ⊢ ➡[h] ⋆ → L1 = ⋆.
+lemma lpr_inv_atom_dx (h) (G): ∀L1. ❪G,L1❫ ⊢ ➡[h,0] ⋆ → L1 = ⋆.
 /2 width=2 by lex_inv_atom_dx/ 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 &
+lemma lpr_inv_bind_dx (h) (G): ∀I2,L1,K2. ❪G,L1❫ ⊢ ➡[h,0] K2.ⓘ[I2] →
+                               ∃∃I1,K1. ❪G,K1❫ ⊢ ➡[h,0] K2 & ❪G,K1❫ ⊢ I1 ➡[h,0] I2 &
                                         L1 = K1.ⓘ[I1].
 /2 width=1 by lex_inv_bind_dx/ 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].
+lemma lpr_inv_unit_sn (h) (G): ∀I,L2,K1. ❪G,K1.ⓤ[I]❫ ⊢ ➡[h,0] L2 →
+                               ∃∃K2. ❪G,K1❫ ⊢ ➡[h,0] 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 &
+lemma lpr_inv_pair_sn (h) (G): ∀I,L2,K1,V1. ❪G,K1.ⓑ[I]V1❫ ⊢ ➡[h,0] L2 →
+                               ∃∃K2,V2. ❪G,K1❫ ⊢ ➡[h,0] K2 & ❪G,K1❫ ⊢ V1 ➡[h,0] 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].
+lemma lpr_inv_unit_dx (h) (G): ∀I,L1,K2. ❪G,L1❫ ⊢ ➡[h,0] K2.ⓤ[I] →
+                               ∃∃K1. ❪G,K1❫ ⊢ ➡[h,0] 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 &
+lemma lpr_inv_pair_dx (h) (G): ∀I,L1,K2,V2. ❪G,L1❫ ⊢ ➡[h,0] K2.ⓑ[I]V2 →
+                               ∃∃K1,V1. ❪G,K1❫ ⊢ ➡[h,0] K2 & ❪G,K1❫ ⊢ V1 ➡[h,0] 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.
+lemma lpr_inv_pair (h) (G): ∀I1,I2,L1,L2,V1,V2. ❪G,L1.ⓑ[I1]V1❫ ⊢ ➡[h,0] L2.ⓑ[I2]V2 →
+                            ∧∧ ❪G,L1❫ ⊢ ➡[h,0] L2 & ❪G,L1❫ ⊢ V1 ➡[h,0] V2 & I1 = I2.
 /2 width=1 by lex_inv_pair/ qed-.
 
 (* Basic_1: removed theorems 3: wcpr0_getl wcpr0_getl_back