update in ground static_2 basic_2 apps_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / cnv_cpm_teqx_conf.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx_conf.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx_conf.ma
index 546223ed6506d24aca24228a1d2d83a9e649c277..d574fb915ac4445c9c9aa2eeca796f6ee427378f 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx_conf.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx_conf.ma
@@ -19,33 +19,33 @@ include "basic_2/dynamic/cnv_cpm_teqx.ma".
 (* CONTEXT-SENSITIVE NATIVE VALIDITY FOR TERMS ******************************)
 
 definition IH_cnv_cpm_teqx_conf_lpr (h) (a): relation3 genv lenv term ≝
-           λG,L0,T0. â\9dªG,L0â\9d« ⊢ T0 ![h,a] →
-           â\88\80n1,T1. â\9dªG,L0â\9d« ⊢ T0 ➡[h,n1] T1 → T0 ≅ T1 →
-           â\88\80n2,T2. â\9dªG,L0â\9d« ⊢ T0 ➡[h,n2] T2 → T0 ≅ T2 →
-           â\88\80L1. â\9dªG,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG,L0â\9d« ⊢ ➡[h,0] L2 →
-           â\88\83â\88\83T. â\9dªG,L1â\9d« â\8a¢ T1 â\9e¡[h,n2-n1] T & T1 â\89\85 T & â\9dªG,L2â\9d« ⊢ T2 ➡[h,n1-n2] T & T2 ≅ T.
+           λG,L0,T0. â\9d¨G,L0â\9d© ⊢ T0 ![h,a] →
+           â\88\80n1,T1. â\9d¨G,L0â\9d© ⊢ T0 ➡[h,n1] T1 → T0 ≅ T1 →
+           â\88\80n2,T2. â\9d¨G,L0â\9d© ⊢ T0 ➡[h,n2] T2 → T0 ≅ T2 →
+           â\88\80L1. â\9d¨G,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G,L0â\9d© ⊢ ➡[h,0] L2 →
+           â\88\83â\88\83T. â\9d¨G,L1â\9d© â\8a¢ T1 â\9e¡[h,n2-n1] T & T1 â\89\85 T & â\9d¨G,L2â\9d© ⊢ T2 ➡[h,n1-n2] T & T2 ≅ T.
 
 (* Diamond propery with restricted rt-transition for terms ******************)
 
 fact cnv_cpm_teqx_conf_lpr_atom_atom_aux (h) (G0) (L1) (L2) (I):
-     â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ â\93ª[I] â\9e¡[h,0] T & â\93ª[I] â\89\85 T & â\9dªG0,L2â\9d« ⊢ ⓪[I] ➡[h,0] T & ⓪[I] ≅ T.
+     â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ â\93ª[I] â\9e¡[h,0] T & â\93ª[I] â\89\85 T & â\9d¨G0,L2â\9d© ⊢ ⓪[I] ➡[h,0] T & ⓪[I] ≅ T.
 #h #G0 #L1 #L2 #I
 /2 width=5 by ex4_intro/
 qed-.
 
 fact cnv_cpm_teqx_conf_lpr_atom_ess_aux (h) (G0) (L1) (L2) (s):
-     â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ â\8b\86s â\9e¡[h,1] T & â\8b\86s â\89\85 T & â\9dªG0,L2â\9d« ⊢ ⋆(⫯[h]s) ➡[h,0] T & ⋆(⫯[h]s) ≅ T.
+     â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ â\8b\86s â\9e¡[h,1] T & â\8b\86s â\89\85 T & â\9d¨G0,L2â\9d© ⊢ ⋆(⫯[h]s) ➡[h,0] T & ⋆(⫯[h]s) ≅ T.
 #h #G0 #L1 #L2 #s
 /3 width=5 by teqg_sort, ex4_intro/
 qed-.
 
 fact cnv_cpm_teqx_conf_lpr_bind_bind_aux (h) (a) (p) (I) (G0) (L0) (V0) (T0):
-     (â\88\80G,L,T. â\9dªG0,L0,â\93\91[p,I]V0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cnv_cpm_teqx_conf_lpr h a G L T) →
-     â\9dªG0,L0â\9d« ⊢ ⓑ[p,I]V0.T0 ![h,a] →
-     â\88\80n1,T1. â\9dªG0,L0.â\93\91[I]V0â\9d« ⊢ T0 ➡[h,n1] T1 → T0 ≅ T1 →
-     â\88\80n2,T2. â\9dªG0,L0.â\93\91[I]V0â\9d« ⊢ T0 ➡[h,n2] T2 → T0 ≅ T2 →
-     â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ â\93\91[p,I]V0.T1 â\9e¡[h,n2-n1] T & â\93\91[p,I]V0.T1 â\89\85 T & â\9dªG0,L2â\9d« ⊢ ⓑ[p,I]V0.T2 ➡[h,n1-n2] T & ⓑ[p,I]V0.T2 ≅ T.
+     (â\88\80G,L,T. â\9d¨G0,L0,â\93\91[p,I]V0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cnv_cpm_teqx_conf_lpr h a G L T) →
+     â\9d¨G0,L0â\9d© ⊢ ⓑ[p,I]V0.T0 ![h,a] →
+     â\88\80n1,T1. â\9d¨G0,L0.â\93\91[I]V0â\9d© ⊢ T0 ➡[h,n1] T1 → T0 ≅ T1 →
+     â\88\80n2,T2. â\9d¨G0,L0.â\93\91[I]V0â\9d© ⊢ T0 ➡[h,n2] T2 → T0 ≅ T2 →
+     â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ â\93\91[p,I]V0.T1 â\9e¡[h,n2-n1] T & â\93\91[p,I]V0.T1 â\89\85 T & â\9d¨G0,L2â\9d© ⊢ ⓑ[p,I]V0.T2 ➡[h,n1-n2] T & ⓑ[p,I]V0.T2 ≅ T.
 #h #a #p #I #G0 #L0 #V0 #T0 #IH #H0
 #n1 #T1 #H1T01 #H2T01 #n2 #T2 #H1T02 #H2T02
 #L1 #HL01 #L2 #HL02
@@ -56,12 +56,12 @@ elim (IH … H1T01 H2T01 … H1T02 H2T02 (L1.ⓑ[I]V0) … (L2.ⓑ[I]V0)) [|*: /
 qed-.
 
 fact cnv_cpm_teqx_conf_lpr_appl_appl_aux (h) (a) (G0) (L0) (V0) (T0):
-     (â\88\80G,L,T. â\9dªG0,L0,â\93\90V0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cnv_cpm_teqx_conf_lpr h a G L T) →
-     â\9dªG0,L0â\9d« ⊢ ⓐV0.T0 ![h,a] →
-     â\88\80n1,T1. â\9dªG0,L0â\9d« ⊢ T0 ➡[h,n1] T1 → T0 ≅ T1 →
-     â\88\80n2,T2. â\9dªG0,L0â\9d« ⊢ T0 ➡[h,n2] T2 → T0 ≅ T2 →
-     â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ â\93\90V0.T1 â\9e¡[h,n2-n1] T & â\93\90V0.T1 â\89\85 T & â\9dªG0,L2â\9d« ⊢ ⓐV0.T2 ➡[h,n1-n2] T & ⓐV0.T2 ≅ T.
+     (â\88\80G,L,T. â\9d¨G0,L0,â\93\90V0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cnv_cpm_teqx_conf_lpr h a G L T) →
+     â\9d¨G0,L0â\9d© ⊢ ⓐV0.T0 ![h,a] →
+     â\88\80n1,T1. â\9d¨G0,L0â\9d© ⊢ T0 ➡[h,n1] T1 → T0 ≅ T1 →
+     â\88\80n2,T2. â\9d¨G0,L0â\9d© ⊢ T0 ➡[h,n2] T2 → T0 ≅ T2 →
+     â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ â\93\90V0.T1 â\9e¡[h,n2-n1] T & â\93\90V0.T1 â\89\85 T & â\9d¨G0,L2â\9d© ⊢ ⓐV0.T2 ➡[h,n1-n2] T & ⓐV0.T2 ≅ T.
 #h #a #G0 #L0 #V0 #T0 #IH #H0
 #n1 #T1 #H1T01 #H2T01 #n2 #T2 #H1T02 #H2T02
 #L1 #HL01 #L2 #HL02
@@ -72,14 +72,14 @@ elim (IH … H1T01 H2T01 … H1T02 H2T02 … HL01 … HL02) [|*: /2 width=1 by f
 qed-.
 
 fact cnv_cpm_teqx_conf_lpr_cast_cast_aux (h) (a) (G0) (L0) (V0) (T0):
-     (â\88\80G,L,T. â\9dªG0,L0,â\93\9dV0.T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cnv_cpm_teqx_conf_lpr h a G L T) →
-     â\9dªG0,L0â\9d« ⊢ ⓝV0.T0 ![h,a] →
-     â\88\80n1,V1. â\9dªG0,L0â\9d« ⊢ V0 ➡[h,n1] V1 → V0 ≅ V1 →
-     â\88\80n2,V2. â\9dªG0,L0â\9d« ⊢ V0 ➡[h,n2] V2 → V0 ≅ V2 →
-     â\88\80T1. â\9dªG0,L0â\9d« ⊢ T0 ➡[h,n1] T1 → T0 ≅ T1 →
-     â\88\80T2. â\9dªG0,L0â\9d« ⊢ T0 ➡[h,n2] T2 → T0 ≅ T2 →
-     â\88\80L1. â\9dªG0,L0â\9d« â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9dªG0,L0â\9d« ⊢ ➡[h,0] L2 →
-     â\88\83â\88\83T. â\9dªG0,L1â\9d« â\8a¢ â\93\9dV1.T1 â\9e¡[h,n2-n1] T & â\93\9dV1.T1 â\89\85 T & â\9dªG0,L2â\9d« ⊢ ⓝV2.T2 ➡[h,n1-n2] T & ⓝV2.T2 ≅ T.
+     (â\88\80G,L,T. â\9d¨G0,L0,â\93\9dV0.T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cnv_cpm_teqx_conf_lpr h a G L T) →
+     â\9d¨G0,L0â\9d© ⊢ ⓝV0.T0 ![h,a] →
+     â\88\80n1,V1. â\9d¨G0,L0â\9d© ⊢ V0 ➡[h,n1] V1 → V0 ≅ V1 →
+     â\88\80n2,V2. â\9d¨G0,L0â\9d© ⊢ V0 ➡[h,n2] V2 → V0 ≅ V2 →
+     â\88\80T1. â\9d¨G0,L0â\9d© ⊢ T0 ➡[h,n1] T1 → T0 ≅ T1 →
+     â\88\80T2. â\9d¨G0,L0â\9d© ⊢ T0 ➡[h,n2] T2 → T0 ≅ T2 →
+     â\88\80L1. â\9d¨G0,L0â\9d© â\8a¢ â\9e¡[h,0] L1 â\86\92 â\88\80L2. â\9d¨G0,L0â\9d© ⊢ ➡[h,0] L2 →
+     â\88\83â\88\83T. â\9d¨G0,L1â\9d© â\8a¢ â\93\9dV1.T1 â\9e¡[h,n2-n1] T & â\93\9dV1.T1 â\89\85 T & â\9d¨G0,L2â\9d© ⊢ ⓝV2.T2 ➡[h,n1-n2] T & ⓝV2.T2 ≅ T.
 #h #a #G0 #L0 #V0 #T0 #IH #H0
 #n1 #V1 #H1V01 #H2V01 #n2 #V2 #H1V02 #H2V02 #T1 #H1T01 #H2T01 #T2 #H1T02 #H2T02
 #L1 #HL01 #L2 #HL02
@@ -91,7 +91,7 @@ elim (IH … H1T01 H2T01 … H1T02 H2T02 … HL01 … HL02) [|*: /2 width=1 by f
 qed-.
 
 fact cnv_cpm_teqx_conf_lpr_aux (h) (a) (G0) (L0) (T0):
-     (â\88\80G,L,T. â\9dªG0,L0,T0â\9d« â¬\82+ â\9dªG,L,Tâ\9d« → IH_cnv_cpm_teqx_conf_lpr h a G L T) →
+     (â\88\80G,L,T. â\9d¨G0,L0,T0â\9d© â¬\82+ â\9d¨G,L,Tâ\9d© → IH_cnv_cpm_teqx_conf_lpr h a G L T) →
      ∀G,L,T. G0 = G → L0 = L → T0 = T → IH_cnv_cpm_teqx_conf_lpr h a G L T.
 #h #a #G0 #L0 #T0 #IH1 #G #L * [| * [| * ]]
 [ #I #HG0 #HL0 #HT0 #HT #n1 #X1 #H1X1 #H2X1 #n2 #X2 #H1X2 #H2X2 #L1 #HL1 #L2 #HL2 destruct