update in ground_2, static_2, basic_2, apps_2, alpha_1

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs.ma
index d532c62bfaeb65a7021d757a10b0c3b620f055c7..ade37fde5a7aa19e2b53c0be3824591792928263 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/lpxs.ma
@@ -28,13 +28,13 @@ interpretation
 (* Basic properties *********************************************************)
 
 (* Basic_2A1: uses: lpxs_pair_refl *)
-lemma lpxs_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¬\88*[h] L2.â\93\98{I}.
+lemma lpxs_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¬\88*[h] L2.â\93\98[I].
 /2 width=1 by lex_bind_refl_dx/ qed.
 
-lemma lpxs_pair (h) (G): â\88\80L1,L2. â¦\83G,L1â¦\84 ⊢ ⬈*[h] L2 →
-                         â\88\80V1,V2. â¦\83G,L1â¦\84 ⊢ V1 ⬈*[h] V2 →
-                         â\88\80I. â¦\83G,L1.â\93\91{I}V1â¦\84 â\8a¢ â¬\88*[h] L2.â\93\91{I}V2.
+lemma lpxs_pair (h) (G): â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ⬈*[h] L2 →
+                         â\88\80V1,V2. â\9dªG,L1â\9d« ⊢ V1 ⬈*[h] V2 →
+                         â\88\80I. â\9dªG,L1.â\93\91[I]V1â\9d« â\8a¢ â¬\88*[h] L2.â\93\91[I]V2.
 /2 width=1 by lex_pair/ qed.
 
 lemma lpxs_refl (h) (G): reflexive … (lpxs h G).
@@ -43,25 +43,25 @@ lemma lpxs_refl (h) (G): reflexive … (lpxs h G).
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: was: lpxs_inv_atom1 *)
-lemma lpxs_inv_atom_sn (h) (G): â\88\80L2. â¦\83G,â\8b\86â¦\84 ⊢ ⬈*[h] L2 → L2 = ⋆.
+lemma lpxs_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-.
 
-lemma lpxs_inv_bind_sn (h) (G): â\88\80I1,L2,K1. â¦\83G,K1.â\93\98{I1}â¦\84 ⊢ ⬈*[h] L2 →
-                                â\88\83â\88\83I2,K2. â¦\83G,K1â¦\84 â\8a¢ â¬\88*[h] K2 & â¦\83G,K1â¦\84 â\8a¢ I1 â¬\88*[h] I2 & L2 = K2.â\93\98{I2}.
+lemma lpxs_inv_bind_sn (h) (G): â\88\80I1,L2,K1. â\9dªG,K1.â\93\98[I1]â\9d« ⊢ ⬈*[h] L2 →
+                                â\88\83â\88\83I2,K2. â\9dªG,K1â\9d« â\8a¢ â¬\88*[h] K2 & â\9dªG,K1â\9d« â\8a¢ I1 â¬\88*[h] I2 & L2 = K2.â\93\98[I2].
 /2 width=1 by lex_inv_bind_sn/ qed-.
 
 (* Basic_2A1: was: lpxs_inv_pair1 *)
-lemma lpxs_inv_pair_sn (h) (G): â\88\80I,L2,K1,V1. â¦\83G,K1.â\93\91{I}V1â¦\84 ⊢ ⬈*[h] L2 →
-                                â\88\83â\88\83K2,V2. â¦\83G,K1â¦\84 â\8a¢ â¬\88*[h] K2 & â¦\83G,K1â¦\84 â\8a¢ V1 â¬\88*[h] V2 & L2 = K2.â\93\91{I}V2.
+lemma lpxs_inv_pair_sn (h) (G): â\88\80I,L2,K1,V1. â\9dªG,K1.â\93\91[I]V1â\9d« ⊢ ⬈*[h] L2 →
+                                â\88\83â\88\83K2,V2. â\9dªG,K1â\9d« â\8a¢ â¬\88*[h] K2 & â\9dªG,K1â\9d« â\8a¢ V1 â¬\88*[h] V2 & L2 = K2.â\93\91[I]V2.
 /2 width=1 by lex_inv_pair_sn/ qed-.
 
 (* Basic_2A1: was: lpxs_inv_atom2 *)
-lemma lpxs_inv_atom_dx (h) (G): â\88\80L1. â¦\83G,L1â¦\84 ⊢ ⬈*[h] ⋆ → L1 = ⋆.
+lemma lpxs_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: lpxs_inv_pair2 *)
-lemma lpxs_inv_pair_dx (h) (G): â\88\80I,L1,K2,V2. â¦\83G,L1â¦\84 â\8a¢ â¬\88*[h] K2.â\93\91{I}V2 →
-                                â\88\83â\88\83K1,V1. â¦\83G,K1â¦\84 â\8a¢ â¬\88*[h] K2 & â¦\83G,K1â¦\84 â\8a¢ V1 â¬\88*[h] V2 & L1 = K1.â\93\91{I}V1.
+lemma lpxs_inv_pair_dx (h) (G): â\88\80I,L1,K2,V2. â\9dªG,L1â\9d« â\8a¢ â¬\88*[h] K2.â\93\91[I]V2 →
+                                â\88\83â\88\83K1,V1. â\9dªG,K1â\9d« â\8a¢ â¬\88*[h] K2 & â\9dªG,K1â\9d« â\8a¢ V1 â¬\88*[h] V2 & L1 = K1.â\93\91[I]V1.
 /2 width=1 by lex_inv_pair_dx/ qed-.
 
 (* Basic eliminators ********************************************************)
@@ -70,12 +70,12 @@ lemma lpxs_inv_pair_dx (h) (G): ∀I,L1,K2,V2. ⦃G,L1⦄ ⊢ ⬈*[h] K2.ⓑ{I}V
 lemma lpxs_ind (h) (G): ∀Q:relation lenv.
                         Q (⋆) (⋆) → (
                           ∀I,K1,K2.
-                          â¦\83G,K1â¦\84 ⊢ ⬈*[h] K2 →
-                          Q K1 K2 → Q (K1.ⓘ{I}) (K2.ⓘ{I})
+                          â\9dªG,K1â\9d« ⊢ ⬈*[h] K2 →
+                          Q K1 K2 → Q (K1.ⓘ[I]) (K2.ⓘ[I])
                         ) → (
                           ∀I,K1,K2,V1,V2.
-                          â¦\83G,K1â¦\84 â\8a¢ â¬\88*[h] K2 â\86\92 â¦\83G,K1â¦\84 ⊢ V1 ⬈*[h] V2 →
-                          Q K1 K2 → Q (K1.ⓑ{I}V1) (K2.ⓑ{I}V2)
+                          â\9dªG,K1â\9d« â\8a¢ â¬\88*[h] K2 â\86\92 â\9dªG,K1â\9d« ⊢ V1 ⬈*[h] V2 →
+                          Q K1 K2 → Q (K1.ⓑ[I]V1) (K2.ⓑ[I]V2)
                         ) →
-                        â\88\80L1,L2. â¦\83G,L1â¦\84 ⊢ ⬈*[h] L2 → Q L1 L2.
+                        â\88\80L1,L2. â\9dªG,L1â\9d« ⊢ ⬈*[h] L2 → Q L1 L2.
 /3 width=4 by lex_ind/ qed-.