update in ground static_2 basic_2 apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs.ma
index a8afc2c236d8c458b705d60e4cd9b6f2b9ee7138..4cf5893f39b2b1895f1af562d4b3dea9215a56d8 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs.ma
@@ -29,16 +29,16 @@ interpretation
 
 lemma cpxs_ind (G) (L) (T1) (Q:predicate …):
       Q T1 →
-      (â\88\80T,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88* T â\86\92 â\9dªG,Lâ\9d« ⊢ T ⬈ T2 → Q T → Q T2) →
-      â\88\80T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈* T2 → Q T2.
+      (â\88\80T,T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\88* T â\86\92 â\9d¨G,Lâ\9d© ⊢ T ⬈ T2 → Q T → Q T2) →
+      â\88\80T2. â\9d¨G,Lâ\9d© ⊢ T1 ⬈* T2 → Q T2.
 #L #G #T1 #Q #HT1 #IHT1 #T2 #HT12
 @(TC_star_ind … HT1 IHT1 … HT12) //
 qed-.
 
 lemma cpxs_ind_dx (G) (L) (T2) (Q:predicate …):
       Q T2 →
-      (â\88\80T1,T. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88 T â\86\92 â\9dªG,Lâ\9d« ⊢ T ⬈* T2 → Q T → Q T1) →
-      â\88\80T1. â\9dªG,Lâ\9d« ⊢ T1 ⬈* T2 → Q T1.
+      (â\88\80T1,T. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\88 T â\86\92 â\9d¨G,Lâ\9d© ⊢ T ⬈* T2 → Q T → Q T1) →
+      â\88\80T1. â\9d¨G,Lâ\9d© ⊢ T1 ⬈* T2 → Q T1.
 #G #L #T2 #Q #HT2 #IHT2 #T1 #HT12
 @(TC_star_ind_dx … HT2 IHT2 … HT12) //
 qed-.
@@ -46,61 +46,61 @@ qed-.
 (* Basic properties *********************************************************)
 
 lemma cpxs_refl (G) (L):
-      â\88\80T. â\9dªG,Lâ\9d« ⊢ T ⬈* T.
+      â\88\80T. â\9d¨G,Lâ\9d© ⊢ T ⬈* T.
 /2 width=1 by inj/ qed.
 
-lemma cpx_cpxs (G) (L): â\88\80T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88 T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ⬈* T2.
+lemma cpx_cpxs (G) (L): â\88\80T1,T2. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\88 T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ⬈* T2.
 /2 width=1 by inj/ qed.
 
 lemma cpxs_strap1 (G) (L):
-      â\88\80T1,T. â\9dªG,Lâ\9d« ⊢ T1 ⬈* T →
-      â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â¬\88 T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ⬈* T2.
+      â\88\80T1,T. â\9d¨G,Lâ\9d© ⊢ T1 ⬈* T →
+      â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T â¬\88 T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ⬈* T2.
 normalize /2 width=3 by step/ qed-.
 
 lemma cpxs_strap2 (G) (L):
-      â\88\80T1,T. â\9dªG,Lâ\9d« ⊢ T1 ⬈ T →
-      â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â¬\88* T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ⬈* T2.
+      â\88\80T1,T. â\9d¨G,Lâ\9d© ⊢ T1 ⬈ T →
+      â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T â¬\88* T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ⬈* T2.
 normalize /2 width=3 by TC_strap/ qed-.
 
 (* Basic_2A1: was just: cpxs_sort *)
 lemma cpxs_qu (G) (L):
-      â\88\80s1,s2. â\9dªG,Lâ\9d« ⊢ ⋆s1 ⬈* ⋆s2.
+      â\88\80s1,s2. â\9d¨G,Lâ\9d© ⊢ ⋆s1 ⬈* ⋆s2.
 /2 width=1 by cpx_cpxs/ qed.
 
 lemma cpxs_bind_dx (G) (L):
-      â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ⬈ V2 →
-      â\88\80I,T1,T2. â\9dªG,L. â\93\91[I]V1â\9d« ⊢ T1 ⬈* T2 →
-      â\88\80p. â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V1.T1 ⬈* ⓑ[p,I]V2.T2.
+      â\88\80V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ⬈ V2 →
+      â\88\80I,T1,T2. â\9d¨G,L. â\93\91[I]V1â\9d© ⊢ T1 ⬈* T2 →
+      â\88\80p. â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V1.T1 ⬈* ⓑ[p,I]V2.T2.
 #G #L #V1 #V2 #HV12 #I #T1 #T2 #HT12 #a @(cpxs_ind_dx … HT12) -T1
 /3 width=3 by cpxs_strap2, cpx_cpxs, cpx_pair_sn, cpx_bind/
 qed.
 
 lemma cpxs_flat_dx (G) (L):
-      â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ⬈ V2 →
-      â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈* T2 →
-      â\88\80I. â\9dªG,Lâ\9d« ⊢ ⓕ[I]V1.T1 ⬈* ⓕ[I]V2.T2.
+      â\88\80V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ⬈ V2 →
+      â\88\80T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ⬈* T2 →
+      â\88\80I. â\9d¨G,Lâ\9d© ⊢ ⓕ[I]V1.T1 ⬈* ⓕ[I]V2.T2.
 #G #L #V1 #V2 #HV12 #T1 #T2 #HT12 @(cpxs_ind … HT12) -T2
 /3 width=5 by cpxs_strap1, cpx_cpxs, cpx_pair_sn, cpx_flat/
 qed.
 
 lemma cpxs_flat_sn (G) (L):
-      â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈ T2 →
-      â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ⬈* V2 →
-      â\88\80I. â\9dªG,Lâ\9d« ⊢ ⓕ[I]V1.T1 ⬈* ⓕ[I]V2.T2.
+      â\88\80T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ⬈ T2 →
+      â\88\80V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ⬈* V2 →
+      â\88\80I. â\9d¨G,Lâ\9d© ⊢ ⓕ[I]V1.T1 ⬈* ⓕ[I]V2.T2.
 #G #L #T1 #T2 #HT12 #V1 #V2 #H @(cpxs_ind … H) -V2
 /3 width=5 by cpxs_strap1, cpx_cpxs, cpx_pair_sn, cpx_flat/
 qed.
 
 lemma cpxs_pair_sn (G) (L):
-      â\88\80I,V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ⬈* V2 →
-      â\88\80T. â\9dªG,Lâ\9d« ⊢ ②[I]V1.T ⬈* ②[I]V2.T.
+      â\88\80I,V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ⬈* V2 →
+      â\88\80T. â\9d¨G,Lâ\9d© ⊢ ②[I]V1.T ⬈* ②[I]V2.T.
 #G #L #I #V1 #V2 #H @(cpxs_ind … H) -V2
 /3 width=3 by cpxs_strap1, cpx_pair_sn/
 qed.
 
 lemma cpxs_zeta (G) (L) (V):
       ∀T1,T. ⇧[1] T ≘ T1 →
-      â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â¬\88* T2 â\86\92 â\9dªG,Lâ\9d« ⊢ +ⓓV.T1 ⬈* T2.
+      â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T â¬\88* T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ +ⓓV.T1 ⬈* T2.
 #G #L #V #T1 #T #HT1 #T2 #H @(cpxs_ind … H) -T2
 /3 width=3 by cpxs_strap1, cpx_cpxs, cpx_zeta/
 qed.
@@ -108,38 +108,38 @@ qed.
 (* Basic_2A1: was: cpxs_zeta *)
 lemma cpxs_zeta_dx (G) (L) (V):
       ∀T2,T. ⇧[1] T2 ≘ T →
-      â\88\80T1. â\9dªG,L.â\93\93Vâ\9d« â\8a¢ T1 â¬\88* T â\86\92 â\9dªG,Lâ\9d« ⊢ +ⓓV.T1 ⬈* T2.
+      â\88\80T1. â\9d¨G,L.â\93\93Vâ\9d© â\8a¢ T1 â¬\88* T â\86\92 â\9d¨G,Lâ\9d© ⊢ +ⓓV.T1 ⬈* T2.
 #G #L #V #T2 #T #HT2 #T1 #H @(cpxs_ind_dx … H) -T1
 /3 width=3 by cpxs_strap2, cpx_cpxs, cpx_bind, cpx_zeta/
 qed.
 
 lemma cpxs_eps (G) (L):
-      â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈* T2 →
-      â\88\80V. â\9dªG,Lâ\9d« ⊢ ⓝV.T1 ⬈* T2.
+      â\88\80T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ⬈* T2 →
+      â\88\80V. â\9d¨G,Lâ\9d© ⊢ ⓝV.T1 ⬈* T2.
 #G #L #T1 #T2 #H @(cpxs_ind … H) -T2
 /3 width=3 by cpxs_strap1, cpx_cpxs, cpx_eps/
 qed.
 
 (* Basic_2A1: was: cpxs_ct *)
 lemma cpxs_ee (G) (L):
-      â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ⬈* V2 →
-      â\88\80T. â\9dªG,Lâ\9d« ⊢ ⓝV1.T ⬈* V2.
+      â\88\80V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ⬈* V2 →
+      â\88\80T. â\9d¨G,Lâ\9d© ⊢ ⓝV1.T ⬈* V2.
 #G #L #V1 #V2 #H @(cpxs_ind … H) -V2
 /3 width=3 by cpxs_strap1, cpx_cpxs, cpx_ee/
 qed.
 
 lemma cpxs_beta_dx (G) (L):
       ∀p,V1,V2,W1,W2,T1,T2.
-      â\9dªG,Lâ\9d« â\8a¢ V1 â¬\88 V2 â\86\92 â\9dªG,L.â\93\9bW1â\9d« â\8a¢ T1 â¬\88* T2 â\86\92 â\9dªG,Lâ\9d« ⊢ W1 ⬈ W2 →
-      â\9dªG,Lâ\9d« ⊢ ⓐV1.ⓛ[p]W1.T1 ⬈* ⓓ[p]ⓝW2.V2.T2.
+      â\9d¨G,Lâ\9d© â\8a¢ V1 â¬\88 V2 â\86\92 â\9d¨G,L.â\93\9bW1â\9d© â\8a¢ T1 â¬\88* T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ W1 ⬈ W2 →
+      â\9d¨G,Lâ\9d© ⊢ ⓐV1.ⓛ[p]W1.T1 ⬈* ⓓ[p]ⓝW2.V2.T2.
 #G #L #p #V1 #V2 #W1 #W2 #T1 #T2 #HV12 * -T2
 /4 width=7 by cpx_cpxs, cpxs_strap1, cpxs_bind_dx, cpxs_flat_dx, cpx_beta/
 qed.
 
 lemma cpxs_theta_dx (G) (L):
       ∀p,V1,V,V2,W1,W2,T1,T2.
-      â\9dªG,Lâ\9d« â\8a¢ V1 â¬\88 V â\86\92 â\87§[1] V â\89\98 V2 â\86\92 â\9dªG,L.â\93\93W1â\9d« ⊢ T1 ⬈* T2 →
-      â\9dªG,Lâ\9d« â\8a¢ W1 â¬\88 W2 â\86\92 â\9dªG,Lâ\9d« ⊢ ⓐV1.ⓓ[p]W1.T1 ⬈* ⓓ[p]W2.ⓐV2.T2.
+      â\9d¨G,Lâ\9d© â\8a¢ V1 â¬\88 V â\86\92 â\87§[1] V â\89\98 V2 â\86\92 â\9d¨G,L.â\93\93W1â\9d© ⊢ T1 ⬈* T2 →
+      â\9d¨G,Lâ\9d© â\8a¢ W1 â¬\88 W2 â\86\92 â\9d¨G,Lâ\9d© ⊢ ⓐV1.ⓓ[p]W1.T1 ⬈* ⓓ[p]W2.ⓐV2.T2.
 #G #L #p #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 * -T2
 /4 width=9 by cpx_cpxs, cpxs_strap1, cpxs_bind_dx, cpxs_flat_dx, cpx_theta/
 qed.
@@ -148,7 +148,7 @@ qed.
 
 (* Basic_2A1: wa just: cpxs_inv_sort1 *)
 lemma cpxs_inv_sort1 (G) (L):
-      â\88\80X2,s1. â\9dªG,Lâ\9d« ⊢ ⋆s1 ⬈* X2 →
+      â\88\80X2,s1. â\9d¨G,Lâ\9d© ⊢ ⋆s1 ⬈* X2 →
       ∃s2. X2 = ⋆s2.
 #G #L #X2 #s1 #H @(cpxs_ind … H) -X2 /2 width=2 by ex_intro/
 #X #X2 #_ #HX2 * #s #H destruct
@@ -156,10 +156,10 @@ elim (cpx_inv_sort1 … HX2) -HX2 #s2 #H destruct /2 width=2 by ex_intro/
 qed-.
 
 lemma cpxs_inv_cast1 (G) (L):
-      â\88\80W1,T1,U2. â\9dªG,Lâ\9d« ⊢ ⓝW1.T1 ⬈* U2 →
-      â\88¨â\88¨ â\88\83â\88\83W2,T2. â\9dªG,Lâ\9d« â\8a¢ W1 â¬\88* W2 & â\9dªG,Lâ\9d« ⊢ T1 ⬈* T2 & U2 = ⓝW2.T2
-       | â\9dªG,Lâ\9d« ⊢ T1 ⬈* U2
-       | â\9dªG,Lâ\9d« ⊢ W1 ⬈* U2.
+      â\88\80W1,T1,U2. â\9d¨G,Lâ\9d© ⊢ ⓝW1.T1 ⬈* U2 →
+      â\88¨â\88¨ â\88\83â\88\83W2,T2. â\9d¨G,Lâ\9d© â\8a¢ W1 â¬\88* W2 & â\9d¨G,Lâ\9d© ⊢ T1 ⬈* T2 & U2 = ⓝW2.T2
+       | â\9d¨G,Lâ\9d© ⊢ T1 ⬈* U2
+       | â\9d¨G,Lâ\9d© ⊢ W1 ⬈* U2.
 #G #L #W1 #T1 #U2 #H @(cpxs_ind … H) -U2 /3 width=5 by or3_intro0, ex3_2_intro/
 #U2 #U #_ #HU2 * /3 width=3 by cpxs_strap1, or3_intro1, or3_intro2/ *
 #W #T #HW1 #HT1 #H destruct