update in ground static_2 basic_2 apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
index 2cfb7ff4de6b73f14f9c19ea4ab52d76ec60dbab..c0e1266ff852e692df265ac53d979ade4f1a6213 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr.ma
@@ -27,8 +27,8 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma lpr_bind (h) (G): â\88\80K1,K2. â\9dªG,K1â\9d« ⊢ ➡[h,0] K2 →
-                        â\88\80I1,I2. â\9dªG,K1â\9d« â\8a¢ I1 â\9e¡[h,0] I2 â\86\92 â\9dªG,K1.â\93\98[I1]â\9d« ⊢ ➡[h,0] K2.ⓘ[I2].
+lemma lpr_bind (h) (G): â\88\80K1,K2. â\9d¨G,K1â\9d© ⊢ ➡[h,0] K2 →
+                        â\88\80I1,I2. â\9d¨G,K1â\9d© â\8a¢ I1 â\9e¡[h,0] I2 â\86\92 â\9d¨G,K1.â\93\98[I1]â\9d© ⊢ ➡[h,0] K2.ⓘ[I2].
 /2 width=1 by lex_bind/ qed.
 
 (* Note: lemma 250 *)
@@ -37,60 +37,60 @@ lemma lpr_refl (h) (G): reflexive … (lpr h 0 G).
 
 (* Advanced properties ******************************************************)
 
-lemma lpr_bind_refl_dx (h) (G): â\88\80K1,K2. â\9dªG,K1â\9d« ⊢ ➡[h,0] K2 →
-                                â\88\80I. â\9dªG,K1.â\93\98[I]â\9d« ⊢ ➡[h,0] K2.ⓘ[I].
+lemma lpr_bind_refl_dx (h) (G): â\88\80K1,K2. â\9d¨G,K1â\9d© ⊢ ➡[h,0] K2 →
+                                â\88\80I. â\9d¨G,K1.â\93\98[I]â\9d© ⊢ ➡[h,0] K2.ⓘ[I].
 /2 width=1 by lex_bind_refl_dx/ qed.
 
-lemma lpr_pair (h) (G): â\88\80K1,K2,V1,V2. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 â\86\92 â\9dªG,K1â\9d« ⊢ V1 ➡[h,0] V2 →
-                        â\88\80I. â\9dªG,K1.â\93\91[I]V1â\9d« ⊢ ➡[h,0] K2.ⓑ[I]V2.
+lemma lpr_pair (h) (G): â\88\80K1,K2,V1,V2. â\9d¨G,K1â\9d© â\8a¢ â\9e¡[h,0] K2 â\86\92 â\9d¨G,K1â\9d© ⊢ V1 ➡[h,0] V2 →
+                        â\88\80I. â\9d¨G,K1.â\93\91[I]V1â\9d© ⊢ ➡[h,0] K2.ⓑ[I]V2.
 /2 width=1 by lex_pair/ qed.
 
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_2A1: was: lpr_inv_atom1 *)
 (* Basic_1: includes: wcpr0_gen_sort *)
-lemma lpr_inv_atom_sn (h) (G): â\88\80L2. â\9dªG,â\8b\86â\9d« ⊢ ➡[h,0] L2 → L2 = ⋆.
+lemma lpr_inv_atom_sn (h) (G): â\88\80L2. â\9d¨G,â\8b\86â\9d© ⊢ ➡[h,0] L2 → L2 = ⋆.
 /2 width=2 by lex_inv_atom_sn/ qed-.
 
-lemma lpr_inv_bind_sn (h) (G): â\88\80I1,L2,K1. â\9dªG,K1.â\93\98[I1]â\9d« ⊢ ➡[h,0] L2 →
-                               â\88\83â\88\83I2,K2. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 & â\9dªG,K1â\9d« ⊢ I1 ➡[h,0] I2 &
+lemma lpr_inv_bind_sn (h) (G): â\88\80I1,L2,K1. â\9d¨G,K1.â\93\98[I1]â\9d© ⊢ ➡[h,0] L2 →
+                               â\88\83â\88\83I2,K2. â\9d¨G,K1â\9d© â\8a¢ â\9e¡[h,0] K2 & â\9d¨G,K1â\9d© ⊢ I1 ➡[h,0] I2 &
                                         L2 = K2.ⓘ[I2].
 /2 width=1 by lex_inv_bind_sn/ qed-.
 
 (* Basic_2A1: was: lpr_inv_atom2 *)
-lemma lpr_inv_atom_dx (h) (G): â\88\80L1. â\9dªG,L1â\9d« ⊢ ➡[h,0] ⋆ → L1 = ⋆.
+lemma lpr_inv_atom_dx (h) (G): â\88\80L1. â\9d¨G,L1â\9d© ⊢ ➡[h,0] ⋆ → L1 = ⋆.
 /2 width=2 by lex_inv_atom_dx/ qed-.
 
-lemma lpr_inv_bind_dx (h) (G): â\88\80I2,L1,K2. â\9dªG,L1â\9d« ⊢ ➡[h,0] K2.ⓘ[I2] →
-                               â\88\83â\88\83I1,K1. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 & â\9dªG,K1â\9d« ⊢ I1 ➡[h,0] I2 &
+lemma lpr_inv_bind_dx (h) (G): â\88\80I2,L1,K2. â\9d¨G,L1â\9d© ⊢ ➡[h,0] K2.ⓘ[I2] →
+                               â\88\83â\88\83I1,K1. â\9d¨G,K1â\9d© â\8a¢ â\9e¡[h,0] K2 & â\9d¨G,K1â\9d© ⊢ I1 ➡[h,0] I2 &
                                         L1 = K1.ⓘ[I1].
 /2 width=1 by lex_inv_bind_dx/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma lpr_inv_unit_sn (h) (G): â\88\80I,L2,K1. â\9dªG,K1.â\93¤[I]â\9d« ⊢ ➡[h,0] L2 →
-                               â\88\83â\88\83K2. â\9dªG,K1â\9d« ⊢ ➡[h,0] K2 & L2 = K2.ⓤ[I].
+lemma lpr_inv_unit_sn (h) (G): â\88\80I,L2,K1. â\9d¨G,K1.â\93¤[I]â\9d© ⊢ ➡[h,0] L2 →
+                               â\88\83â\88\83K2. â\9d¨G,K1â\9d© ⊢ ➡[h,0] K2 & L2 = K2.ⓤ[I].
 /2 width=1 by lex_inv_unit_sn/ qed-.
 
 (* Basic_2A1: was: lpr_inv_pair1 *)
 (* Basic_1: includes: wcpr0_gen_head *)
-lemma lpr_inv_pair_sn (h) (G): â\88\80I,L2,K1,V1. â\9dªG,K1.â\93\91[I]V1â\9d« ⊢ ➡[h,0] L2 →
-                               â\88\83â\88\83K2,V2. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 & â\9dªG,K1â\9d« ⊢ V1 ➡[h,0] V2 &
+lemma lpr_inv_pair_sn (h) (G): â\88\80I,L2,K1,V1. â\9d¨G,K1.â\93\91[I]V1â\9d© ⊢ ➡[h,0] L2 →
+                               â\88\83â\88\83K2,V2. â\9d¨G,K1â\9d© â\8a¢ â\9e¡[h,0] K2 & â\9d¨G,K1â\9d© ⊢ V1 ➡[h,0] V2 &
                                         L2 = K2.ⓑ[I]V2.
 /2 width=1 by lex_inv_pair_sn/ qed-.
 
-lemma lpr_inv_unit_dx (h) (G): â\88\80I,L1,K2. â\9dªG,L1â\9d« ⊢ ➡[h,0] K2.ⓤ[I] →
-                               â\88\83â\88\83K1. â\9dªG,K1â\9d« ⊢ ➡[h,0] K2 & L1 = K1.ⓤ[I].
+lemma lpr_inv_unit_dx (h) (G): â\88\80I,L1,K2. â\9d¨G,L1â\9d© ⊢ ➡[h,0] K2.ⓤ[I] →
+                               â\88\83â\88\83K1. â\9d¨G,K1â\9d© ⊢ ➡[h,0] K2 & L1 = K1.ⓤ[I].
 /2 width=1 by lex_inv_unit_dx/ qed-.
 
 (* Basic_2A1: was: lpr_inv_pair2 *)
-lemma lpr_inv_pair_dx (h) (G): â\88\80I,L1,K2,V2. â\9dªG,L1â\9d« ⊢ ➡[h,0] K2.ⓑ[I]V2 →
-                               â\88\83â\88\83K1,V1. â\9dªG,K1â\9d« â\8a¢ â\9e¡[h,0] K2 & â\9dªG,K1â\9d« ⊢ V1 ➡[h,0] V2 &
+lemma lpr_inv_pair_dx (h) (G): â\88\80I,L1,K2,V2. â\9d¨G,L1â\9d© ⊢ ➡[h,0] K2.ⓑ[I]V2 →
+                               â\88\83â\88\83K1,V1. â\9d¨G,K1â\9d© â\8a¢ â\9e¡[h,0] K2 & â\9d¨G,K1â\9d© ⊢ V1 ➡[h,0] V2 &
                                         L1 = K1.ⓑ[I]V1.
 /2 width=1 by lex_inv_pair_dx/ qed-.
 
-lemma lpr_inv_pair (h) (G): â\88\80I1,I2,L1,L2,V1,V2. â\9dªG,L1.â\93\91[I1]V1â\9d« ⊢ ➡[h,0] L2.ⓑ[I2]V2 →
-                            â\88§â\88§ â\9dªG,L1â\9d« â\8a¢ â\9e¡[h,0] L2 & â\9dªG,L1â\9d« ⊢ V1 ➡[h,0] V2 & I1 = I2.
+lemma lpr_inv_pair (h) (G): â\88\80I1,I2,L1,L2,V1,V2. â\9d¨G,L1.â\93\91[I1]V1â\9d© ⊢ ➡[h,0] L2.ⓑ[I2]V2 →
+                            â\88§â\88§ â\9d¨G,L1â\9d© â\8a¢ â\9e¡[h,0] L2 & â\9d¨G,L1â\9d© ⊢ V1 ➡[h,0] V2 & I1 = I2.
 /2 width=1 by lex_inv_pair/ qed-.
 
 (* Basic_1: removed theorems 3: wcpr0_getl wcpr0_getl_back