update in ground_2, static_2, basic_2, apps_2, alpha_1

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / lpx.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
index 14d34b21a87bede5bed3119697c4a13d8d6ef545..4363fb103de399deaf28adc127d39411ab31b3f0 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpx.ma
@@ -27,8 +27,8 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma lpx_bind (h) (G): â\88\80K1,K2. â¦\83G,K1â¦\84 ⊢ ⬈[h] K2 →
-                        â\88\80I1,I2. â¦\83G,K1â¦\84 â\8a¢ I1 â¬\88[h] I2 â\86\92 â¦\83G,K1.â\93\98{I1}â¦\84 â\8a¢ â¬\88[h] K2.â\93\98{I2}.
+lemma lpx_bind (h) (G): â\88\80K1,K2. â\9dªG,K1â\9d« ⊢ ⬈[h] K2 →
+                        â\88\80I1,I2. â\9dªG,K1â\9d« â\8a¢ I1 â¬\88[h] I2 â\86\92 â\9dªG,K1.â\93\98[I1]â\9d« â\8a¢ â¬\88[h] K2.â\93\98[I2].
 /2 width=1 by lex_bind/ qed.
 
 lemma lpx_refl (h) (G): reflexive … (lpx h G).
@@ -36,56 +36,56 @@ lemma lpx_refl (h) (G): reflexive … (lpx h G).
 
 (* Advanced properties ******************************************************)
 
-lemma lpx_bind_refl_dx (h) (G): â\88\80K1,K2. â¦\83G,K1â¦\84 ⊢ ⬈[h] K2 →
-                                â\88\80I. â¦\83G,K1.â\93\98{I}â¦\84 â\8a¢ â¬\88[h] K2.â\93\98{I}.
+lemma lpx_bind_refl_dx (h) (G): â\88\80K1,K2. â\9dªG,K1â\9d« ⊢ ⬈[h] K2 →
+                                â\88\80I. â\9dªG,K1.â\93\98[I]â\9d« â\8a¢ â¬\88[h] K2.â\93\98[I].
 /2 width=1 by lex_bind_refl_dx/ qed.
 
-lemma lpx_pair (h) (G): â\88\80K1,K2. â¦\83G,K1â¦\84 â\8a¢ â¬\88[h] K2 â\86\92 â\88\80V1,V2. â¦\83G,K1â¦\84 ⊢ V1 ⬈[h] V2 →
-                        â\88\80I.â¦\83G,K1.â\93\91{I}V1â¦\84 â\8a¢ â¬\88[h] K2.â\93\91{I}V2.
+lemma lpx_pair (h) (G): â\88\80K1,K2. â\9dªG,K1â\9d« â\8a¢ â¬\88[h] K2 â\86\92 â\88\80V1,V2. â\9dªG,K1â\9d« ⊢ V1 ⬈[h] V2 →
+                        â\88\80I.â\9dªG,K1.â\93\91[I]V1â\9d« â\8a¢ â¬\88[h] K2.â\93\91[I]V2.
 /2 width=1 by lex_pair/ qed.
 
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: was: lpx_inv_atom1 *)
-lemma lpx_inv_atom_sn (h) (G): â\88\80L2. â¦\83G,â\8b\86â¦\84 ⊢ ⬈[h] L2 → L2 = ⋆.
+lemma lpx_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 lpx_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 ⊢ I1 ⬈[h] I2 &
-                                        L2 = K2.ⓘ{I2}.
+lemma lpx_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« ⊢ I1 ⬈[h] I2 &
+                                        L2 = K2.ⓘ[I2].
 /2 width=1 by lex_inv_bind_sn/ qed-.
 
 (* Basic_2A1: was: lpx_inv_atom2 *)
-lemma lpx_inv_atom_dx: â\88\80h,G,L1. â¦\83G,L1â¦\84 ⊢ ⬈[h] ⋆ → L1 = ⋆.
+lemma lpx_inv_atom_dx: â\88\80h,G,L1. â\9dªG,L1â\9d« ⊢ ⬈[h] ⋆ → L1 = ⋆.
 /2 width=2 by lex_inv_atom_dx/ qed-.
 
-lemma lpx_inv_bind_dx (h) (G): â\88\80I2,L1,K2. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h] K2.â\93\98{I2} →
-                               â\88\83â\88\83I1,K1. â¦\83G,K1â¦\84 â\8a¢ â¬\88[h] K2 & â¦\83G,K1â¦\84 ⊢ I1 ⬈[h] I2 &
-                                        L1 = K1.ⓘ{I1}.
+lemma lpx_inv_bind_dx (h) (G): â\88\80I2,L1,K2. â\9dªG,L1â\9d« â\8a¢ â¬\88[h] K2.â\93\98[I2] →
+                               â\88\83â\88\83I1,K1. â\9dªG,K1â\9d« â\8a¢ â¬\88[h] K2 & â\9dªG,K1â\9d« ⊢ I1 ⬈[h] I2 &
+                                        L1 = K1.ⓘ[I1].
 /2 width=1 by lex_inv_bind_dx/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma lpx_inv_unit_sn (h) (G): â\88\80I,L2,K1. â¦\83G,K1.â\93¤{I}â¦\84 ⊢ ⬈[h] L2 →
-                               â\88\83â\88\83K2. â¦\83G,K1â¦\84 â\8a¢ â¬\88[h] K2 & L2 = K2.â\93¤{I}.
+lemma lpx_inv_unit_sn (h) (G): â\88\80I,L2,K1. â\9dªG,K1.â\93¤[I]â\9d« ⊢ ⬈[h] L2 →
+                               â\88\83â\88\83K2. â\9dªG,K1â\9d« â\8a¢ â¬\88[h] K2 & L2 = K2.â\93¤[I].
 /2 width=1 by lex_inv_unit_sn/ qed-.
 
 (* Basic_2A1: was: lpx_inv_pair1 *)
-lemma lpx_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 ⊢ V1 ⬈[h] V2 &
-                                        L2 = K2.ⓑ{I}V2.
+lemma lpx_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« ⊢ V1 ⬈[h] V2 &
+                                        L2 = K2.ⓑ[I]V2.
 /2 width=1 by lex_inv_pair_sn/ qed-.
 
-lemma lpx_inv_unit_dx (h) (G): â\88\80I,L1,K2. â¦\83G,L1â¦\84 â\8a¢ â¬\88[h] K2.â\93¤{I} →
-                               â\88\83â\88\83K1. â¦\83G,K1â¦\84 â\8a¢ â¬\88[h] K2 & L1 = K1.â\93¤{I}.
+lemma lpx_inv_unit_dx (h) (G): â\88\80I,L1,K2. â\9dªG,L1â\9d« â\8a¢ â¬\88[h] K2.â\93¤[I] →
+                               â\88\83â\88\83K1. â\9dªG,K1â\9d« â\8a¢ â¬\88[h] K2 & L1 = K1.â\93¤[I].
 /2 width=1 by lex_inv_unit_dx/ qed-.
 
 (* Basic_2A1: was: lpx_inv_pair2 *)
-lemma lpx_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 ⊢ V1 ⬈[h] V2 &
-                                        L1 = K1.ⓑ{I}V1.
+lemma lpx_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« ⊢ V1 ⬈[h] V2 &
+                                        L1 = K1.ⓑ[I]V1.
 /2 width=1 by lex_inv_pair_dx/ qed-.
 
-lemma lpx_inv_pair (h) (G): â\88\80I1,I2,L1,L2,V1,V2. â¦\83G,L1.â\93\91{I1}V1â¦\84 â\8a¢ â¬\88[h] L2.â\93\91{I2}V2 →
-                            â\88§â\88§ â¦\83G,L1â¦\84 â\8a¢ â¬\88[h] L2 & â¦\83G,L1â¦\84 ⊢ V1 ⬈[h] V2 & I1 = I2.
+lemma lpx_inv_pair (h) (G): â\88\80I1,I2,L1,L2,V1,V2. â\9dªG,L1.â\93\91[I1]V1â\9d« â\8a¢ â¬\88[h] L2.â\93\91[I2]V2 →
+                            â\88§â\88§ â\9dªG,L1â\9d« â\8a¢ â¬\88[h] L2 & â\9dªG,L1â\9d« ⊢ V1 ⬈[h] V2 & I1 = I2.
 /2 width=1 by lex_inv_pair/ qed-.