update in basic_2 and apps_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / lprs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs.ma
index d4061da3936799e108668242ee7bbc35c04a6bbf..1d7f3a1805a03623a2fa758f6e08a1f08286669e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs.ma
@@ -12,54 +12,54 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predsnstar_4.ma".
+include "basic_2/notation/relations/predsnstar_5.ma".
 include "static_2/relocation/lex.ma".
 include "basic_2/rt_computation/cprs_ext.ma".
 
 (* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
 
-definition lprs (h) (G): relation lenv ≝
-                         lex (λL.cpms h G L 0).
+definition lprs (h) (n) (G): relation lenv ≝
+           lex (λL.cpms h G L n).
 
 interpretation
    "parallel r-computation on all entries (local environment)"
-   'PRedSnStar h G L1 L2 = (lprs h G L1 L2).
+   'PRedSnStar h n G L1 L2 = (lprs h n G L1 L2).
 
 (* Basic properties *********************************************************)
 
 (* Basic_2A1: uses: lprs_pair_refl *)
-lemma lprs_bind_refl_dx (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ➡*[h] L2 →
-                                 ∀I. ❪G,L1.ⓘ[I]❫ ⊢ ➡*[h] L2.ⓘ[I].
+lemma lprs_bind_refl_dx (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ➡*[h,0] L2 →
+                                 ∀I. ❪G,L1.ⓘ[I]❫ ⊢ ➡*[h,0] L2.ⓘ[I].
 /2 width=1 by lex_bind_refl_dx/ qed.
 
-lemma lprs_pair (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ➡*[h] L2 →
-                         ∀V1,V2. ❪G,L1❫ ⊢ V1 ➡*[h] V2 →
-                         ∀I. ❪G,L1.ⓑ[I]V1❫ ⊢ ➡*[h] L2.ⓑ[I]V2.
+lemma lprs_pair (h) (G): ∀L1,L2. ❪G,L1❫ ⊢ ➡*[h,0] L2 →
+                         ∀V1,V2. ❪G,L1❫ ⊢ V1 ➡*[h,0] V2 →
+                         ∀I. ❪G,L1.ⓑ[I]V1❫ ⊢ ➡*[h,0] L2.ⓑ[I]V2.
 /2 width=1 by lex_pair/ qed.
 
-lemma lprs_refl (h) (G): ∀L. ❪G,L❫ ⊢ ➡*[h] L.
+lemma lprs_refl (h) (G): ∀L. ❪G,L❫ ⊢ ➡*[h,0] L.
 /2 width=1 by lex_refl/ qed.
 
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: uses: lprs_inv_atom1 *)
-lemma lprs_inv_atom_sn (h) (G): ∀L2. ❪G,⋆❫ ⊢ ➡*[h] L2 → L2 = ⋆.
+lemma lprs_inv_atom_sn (h) (G): ∀L2. ❪G,⋆❫ ⊢ ➡*[h,0] L2 → L2 = ⋆.
 /2 width=2 by lex_inv_atom_sn/ qed-.
 
 (* Basic_2A1: was: lprs_inv_pair1 *)
 lemma lprs_inv_pair_sn (h) (G):
-                       ∀I,K1,L2,V1. ❪G,K1.ⓑ[I]V1❫ ⊢ ➡*[h] L2 →
-                       ∃∃K2,V2. ❪G,K1❫ ⊢ ➡*[h] K2 & ❪G,K1❫ ⊢ V1 ➡*[h] V2 & L2 = K2.ⓑ[I]V2.
+                       ∀I,K1,L2,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-.
 
 (* Basic_2A1: uses: lprs_inv_atom2 *)
-lemma lprs_inv_atom_dx (h) (G): ∀L1. ❪G,L1❫ ⊢ ➡*[h] ⋆ → L1 = ⋆.
+lemma lprs_inv_atom_dx (h) (G): ∀L1. ❪G,L1❫ ⊢ ➡*[h,0] ⋆ → L1 = ⋆.
 /2 width=2 by lex_inv_atom_dx/ qed-.
 
 (* Basic_2A1: was: lprs_inv_pair2 *)
 lemma lprs_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.
+                       ∀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-.
 
 (* Basic eliminators ********************************************************)
@@ -68,12 +68,12 @@ lemma lprs_inv_pair_dx (h) (G):
 lemma lprs_ind (h) (G): ∀Q:relation lenv.
                         Q (⋆) (⋆) → (
                           ∀I,K1,K2.
-                          ❪G,K1❫ ⊢ ➡*[h] K2 →
+                          ❪G,K1❫ ⊢ ➡*[h,0] K2 →
                           Q K1 K2 → Q (K1.ⓘ[I]) (K2.ⓘ[I])
                         ) → (
                           ∀I,K1,K2,V1,V2.
-                          ❪G,K1❫ ⊢ ➡*[h] K2 → ❪G,K1❫ ⊢ V1 ➡*[h] V2 →
+                          ❪G,K1❫ ⊢ ➡*[h,0] K2 → ❪G,K1❫ ⊢ V1 ➡*[h,0] V2 →
                           Q K1 K2 → Q (K1.ⓑ[I]V1) (K2.ⓑ[I]V2)
                         ) →
-                        ∀L1,L2. ❪G,L1❫ ⊢ ➡*[h] L2 → Q L1 L2.
+                        ∀L1,L2. ❪G,L1❫ ⊢ ➡*[h,0] L2 → Q L1 L2.
 /3 width=4 by lex_ind/ qed-.