update in ground_2, static_2, basic_2, apps_2, alpha_1

[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 c06e0278d02249239453d0b543644278b47874c2..d4061da3936799e108668242ee7bbc35c04a6bbf 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs.ma
@@ -13,7 +13,7 @@
 (**************************************************************************)
 
 include "basic_2/notation/relations/predsnstar_4.ma".
-include "basic_2/relocation/lex.ma".
+include "static_2/relocation/lex.ma".
 include "basic_2/rt_computation/cprs_ext.ma".
 
 (* PARALLEL R-COMPUTATION FOR FULL LOCAL ENVIRONMENTS ***********************)
@@ -27,20 +27,53 @@ interpretation
 
 (* 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): â\88\80L1,L2. â¦\83G, L1â¦\84 ⊢ ➡*[h] L2 →
-                                 â\88\80I. â¦\83G, L1.â\93\98{I}â¦\84 â\8a¢ â\9e¡*[h] L2.â\93\98{I}.
+lemma lprs_bind_refl_dx (h) (G): â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ➡*[h] L2 →
+                                 â\88\80I. â\9dªG,L1.â\93\98[I]â\9d« â\8a¢ â\9e¡*[h] L2.â\93\98[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.
+/2 width=1 by lex_pair/ qed.
+
+lemma lprs_refl (h) (G): ∀L. ❪G,L❫ ⊢ ➡*[h] L.
+/2 width=1 by lex_refl/ qed.
+
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: uses: lprs_inv_atom1 *)
-lemma lprs_inv_atom_sn (h) (G): â\88\80L2. â¦\83G, â\8b\86â¦\84 ⊢ ➡*[h] L2 → L2 = ⋆.
+lemma lprs_inv_atom_sn (h) (G): â\88\80L2. â\9dªG,â\8b\86â\9d« ⊢ ➡*[h] 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.
+/2 width=1 by lex_inv_pair_sn/ qed-.
+
 (* Basic_2A1: uses: lprs_inv_atom2 *)
-lemma lprs_inv_atom_dx (h) (G): â\88\80L1. â¦\83G, L1â¦\84 ⊢ ➡*[h] ⋆ → L1 = ⋆.
+lemma lprs_inv_atom_dx (h) (G): â\88\80L1. â\9dªG,L1â\9d« ⊢ ➡*[h] ⋆ → 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.
+/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] K2 →
+                          Q K1 K2 → Q (K1.ⓘ[I]) (K2.ⓘ[I])
+                        ) → (
+                          ∀I,K1,K2,V1,V2.
+                          ❪G,K1❫ ⊢ ➡*[h] K2 → ❪G,K1❫ ⊢ V1 ➡*[h] V2 →
+                          Q K1 K2 → Q (K1.ⓑ[I]V1) (K2.ⓑ[I]V2)
+                        ) →
+                        ∀L1,L2. ❪G,L1❫ ⊢ ➡*[h] L2 → Q L1 L2.
+/3 width=4 by lex_ind/ qed-.