X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Flprs.ma;h=1d7f3a1805a03623a2fa758f6e08a1f08286669e;hb=ca7327c20c6031829fade8bb84a3a1bb66113f54;hp=02f4a101c42f44486a3676df14672f3aff673d0d;hpb=8f5533bd34e93eee2a14cdcfd0595be65651bfa7;p=helm.git

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 02f4a101c..1d7f3a180 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs.ma
@@ -12,35 +12,68 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/notation/relations/predsnstar_4.ma".
-include "basic_2/relocation/lex.ma".
-include "basic_2/rt_computation/cpms.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 *********************************************************)
 
-lemma lprs_refl (h) (G): ∀L. ⦃G, L⦄ ⊢ ➡*[h] L.
-/2 width=1 by lex_refl/ qed.
-
 (* 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,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,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,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,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 ********************************************************)
+
+(* Basic_2A1: was: lprs_ind_alt *)
+lemma lprs_ind (h) (G): ∀Q:relation lenv.
+                        Q (⋆) (⋆) → (
+                          ∀I,K1,K2.
+                          ❪G,K1❫ ⊢ ➡*[h,0] K2 →
+                          Q K1 K2 → Q (K1.ⓘ[I]) (K2.ⓘ[I])
+                        ) → (
+                          ∀I,K1,K2,V1,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,0] L2 → Q L1 L2.
+/3 width=4 by lex_ind/ qed-.