update in ground static_2 basic_2 apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_cpxs.ma
index 92146c7eeb0e3abee1e10afb5bf90dff45e5aeff..761dc2ac5ce63f01f6bb47d464358e86101569e2 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_cpxs.ma
@@ -25,51 +25,51 @@ theorem cpxs_trans (G) (L):
 normalize /2 width=3 by trans_TC/ qed-.
 
 theorem cpxs_bind (G) (L):
-        â\88\80p,I,V1,V2,T1,T2. â\9dªG,L.â\93\91[I]V1â\9d« ⊢ T1 ⬈* T2 →
-        â\9dªG,Lâ\9d« ⊢ V1 ⬈* V2 →
-        â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V1.T1 ⬈* ⓑ[p,I]V2.T2.
+        â\88\80p,I,V1,V2,T1,T2. â\9d¨G,L.â\93\91[I]V1â\9d© ⊢ T1 ⬈* T2 →
+        â\9d¨G,Lâ\9d© ⊢ V1 ⬈* V2 →
+        â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V1.T1 ⬈* ⓑ[p,I]V2.T2.
 #G #L #p #I #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2
 /3 width=5 by cpxs_trans, cpxs_bind_dx/
 qed.
 
 theorem cpxs_flat (G) (L):
-        â\88\80I,V1,V2,T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈* T2 →
-        â\9dªG,Lâ\9d« ⊢ V1 ⬈* V2 →
-        â\9dªG,Lâ\9d« ⊢ ⓕ[I]V1.T1 ⬈* ⓕ[I]V2.T2.
+        â\88\80I,V1,V2,T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ⬈* T2 →
+        â\9d¨G,Lâ\9d© ⊢ V1 ⬈* V2 →
+        â\9d¨G,Lâ\9d© ⊢ ⓕ[I]V1.T1 ⬈* ⓕ[I]V2.T2.
 #G #L #I #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2
 /3 width=5 by cpxs_trans, cpxs_flat_dx/
 qed.
 
 theorem cpxs_beta_rc (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 #HT12 #H @(cpxs_ind … H) -W2
 /4 width=5 by cpxs_trans, cpxs_beta_dx, cpxs_bind_dx, cpx_pair_sn/
 qed.
 
 theorem cpxs_beta (G) (L):
         ∀p,V1,V2,W1,W2,T1,T2.
-        â\9dªG,L.â\93\9bW1â\9d« â\8a¢ T1 â¬\88* T2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ W1 â¬\88* W2 â\86\92 â\9dªG,Lâ\9d« ⊢ V1 ⬈* V2 →
-        â\9dªG,Lâ\9d« ⊢ ⓐV1.ⓛ[p]W1.T1 ⬈* ⓓ[p]ⓝW2.V2.T2.
+        â\9d¨G,L.â\93\9bW1â\9d© â\8a¢ T1 â¬\88* T2 â\86\92 â\9d¨G,Lâ\9d© â\8a¢ W1 â¬\88* W2 â\86\92 â\9d¨G,Lâ\9d© ⊢ V1 ⬈* V2 →
+        â\9d¨G,Lâ\9d© ⊢ ⓐV1.ⓛ[p]W1.T1 ⬈* ⓓ[p]ⓝW2.V2.T2.
 #G #L #p #V1 #V2 #W1 #W2 #T1 #T2 #HT12 #HW12 #H @(cpxs_ind … H) -V2
 /4 width=5 by cpxs_trans, cpxs_beta_rc, cpxs_bind_dx, cpx_flat/
 qed.
 
 theorem cpxs_theta_rc (G) (L):
         ∀p,V1,V,V2,W1,W2,T1,T2.
-        â\9dªG,Lâ\9d« ⊢ V1 ⬈ V → ⇧[1] V ≘ V2 →
-        â\9dªG,L.â\93\93W1â\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© ⊢ V1 ⬈ V → ⇧[1] V ≘ V2 →
+        â\9d¨G,L.â\93\93W1â\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 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 #HT12 #H @(cpxs_ind … H) -W2
 /3 width=5 by cpxs_trans, cpxs_theta_dx, cpxs_bind_dx/
 qed.
 
 theorem cpxs_theta (G) (L):
         ∀p,V1,V,V2,W1,W2,T1,T2.
-        â\87§[1] V â\89\98 V2 â\86\92 â\9dªG,Lâ\9d« ⊢ W1 ⬈* W2 →
-        â\9dªG,L.â\93\93W1â\9d« â\8a¢ T1 â¬\88* T2 â\86\92 â\9dªG,Lâ\9d« ⊢ V1 ⬈* V →
-        â\9dªG,Lâ\9d« ⊢ ⓐV1.ⓓ[p]W1.T1 ⬈* ⓓ[p]W2.ⓐV2.T2.
+        â\87§[1] V â\89\98 V2 â\86\92 â\9d¨G,Lâ\9d© ⊢ W1 ⬈* W2 →
+        â\9d¨G,L.â\93\93W1â\9d© â\8a¢ T1 â¬\88* T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ V1 ⬈* V →
+        â\9d¨G,Lâ\9d© ⊢ ⓐV1.ⓓ[p]W1.T1 ⬈* ⓓ[p]W2.ⓐV2.T2.
 #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV2 #HW12 #HT12 #H @(TC_ind_dx … V1 H) -V1
 /3 width=5 by cpxs_trans, cpxs_theta_rc, cpxs_flat_dx/
 qed.
@@ -77,10 +77,10 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 lemma cpxs_inv_appl1 (G) (L):
-      â\88\80V1,T1,U2. â\9dªG,Lâ\9d« ⊢ ⓐV1.T1 ⬈* U2 →
-      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â¬\88* V2 & â\9dªG,Lâ\9d« ⊢ T1 ⬈* T2 & U2 = ⓐV2.T2
-       | â\88\83â\88\83p,W,T. â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88* â\93\9b[p]W.T & â\9dªG,Lâ\9d« ⊢ ⓓ[p]ⓝW.V1.T ⬈* U2
-       | â\88\83â\88\83p,V0,V2,V,T. â\9dªG,Lâ\9d« â\8a¢ V1 â¬\88* V0 & â\87§[1] V0 â\89\98 V2 & â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88* â\93\93[p]V.T & â\9dªG,Lâ\9d« ⊢ ⓓ[p]V.ⓐV2.T ⬈* U2.
+      â\88\80V1,T1,U2. â\9d¨G,Lâ\9d© ⊢ ⓐV1.T1 ⬈* U2 →
+      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â¬\88* V2 & â\9d¨G,Lâ\9d© ⊢ T1 ⬈* T2 & U2 = ⓐV2.T2
+       | â\88\83â\88\83p,W,T. â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\88* â\93\9b[p]W.T & â\9d¨G,Lâ\9d© ⊢ ⓓ[p]ⓝW.V1.T ⬈* U2
+       | â\88\83â\88\83p,V0,V2,V,T. â\9d¨G,Lâ\9d© â\8a¢ V1 â¬\88* V0 & â\87§[1] V0 â\89\98 V2 & â\9d¨G,Lâ\9d© â\8a¢ T1 â¬\88* â\93\93[p]V.T & â\9d¨G,Lâ\9d© ⊢ ⓓ[p]V.ⓐV2.T ⬈* U2.
 #G #L #V1 #T1 #U2 #H @(cpxs_ind … H) -U2 [ /3 width=5 by or3_intro0, ex3_2_intro/ ]
 #U #U2 #_ #HU2 * *
 [ #V0 #T0 #HV10 #HT10 #H destruct