update in ground static_2 basic_2 apps_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_cpms.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_cpms.ma
index 6b1f5ddc0e68cce3e47a886082e3ca69e2a28375..0f3f83ab5931aed4f1caa3fbfc1a2be1e23c8585 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_cpms.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_cpms.ma
@@ -24,9 +24,9 @@ include "basic_2/rt_computation/cprs.ma".
 
 (* Basic_2A1: includes: cprs_bind *)
 theorem cpms_bind (h) (n) (G) (L):
-                  â\88\80I,V1,T1,T2. â\9dªG,L.â\93\91[I]V1â\9d« ⊢ T1 ➡*[h,n] T2 →
-                  â\88\80V2. â\9dªG,Lâ\9d« ⊢ V1 ➡*[h,0] V2 →
-                  â\88\80p. â\9dªG,Lâ\9d« ⊢ ⓑ[p,I]V1.T1 ➡*[h,n] ⓑ[p,I]V2.T2.
+                  â\88\80I,V1,T1,T2. â\9d¨G,L.â\93\91[I]V1â\9d© ⊢ T1 ➡*[h,n] T2 →
+                  â\88\80V2. â\9d¨G,Lâ\9d© ⊢ V1 ➡*[h,0] V2 →
+                  â\88\80p. â\9d¨G,Lâ\9d© ⊢ ⓑ[p,I]V1.T1 ➡*[h,n] ⓑ[p,I]V2.T2.
 #h #n #G #L #I #V1 #T1 #T2 #HT12 #V2 #H @(cprs_ind_dx … H) -V2
 [ /2 width=1 by cpms_bind_dx/
 | #V #V2 #_ #HV2 #IH #p >(plus_n_O … n) -HT12
@@ -35,9 +35,9 @@ theorem cpms_bind (h) (n) (G) (L):
 qed.
 
 theorem cpms_appl (h) (n) (G) (L):
-                  â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,n] T2 →
-                  â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡*[h,0] V2 →
-                  â\9dªG,Lâ\9d« ⊢ ⓐV1.T1 ➡*[h,n] ⓐV2.T2.
+                  â\88\80T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,n] T2 →
+                  â\88\80V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ➡*[h,0] V2 →
+                  â\9d¨G,Lâ\9d© ⊢ ⓐV1.T1 ➡*[h,n] ⓐV2.T2.
 #h #n #G #L #T1 #T2 #HT12 #V1 #V2 #H @(cprs_ind_dx … H) -V2
 [ /2 width=1 by cpms_appl_dx/
 | #V #V2 #_ #HV2 #IH >(plus_n_O … n) -HT12
@@ -47,10 +47,10 @@ qed.
 
 (* Basic_2A1: includes: cprs_beta_rc *)
 theorem cpms_beta_rc (h) (n) (G) (L):
-                     â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡[h,0] V2 →
-                     â\88\80W1,T1,T2. â\9dªG,L.â\93\9bW1â\9d« ⊢ T1 ➡*[h,n] T2 →
-                     â\88\80W2. â\9dªG,Lâ\9d« ⊢ W1 ➡*[h,0] W2 →
-                     â\88\80p. â\9dªG,Lâ\9d« ⊢ ⓐV1.ⓛ[p]W1.T1 ➡*[h,n] ⓓ[p]ⓝW2.V2.T2.
+                     â\88\80V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ➡[h,0] V2 →
+                     â\88\80W1,T1,T2. â\9d¨G,L.â\93\9bW1â\9d© ⊢ T1 ➡*[h,n] T2 →
+                     â\88\80W2. â\9d¨G,Lâ\9d© ⊢ W1 ➡*[h,0] W2 →
+                     â\88\80p. â\9d¨G,Lâ\9d© ⊢ ⓐV1.ⓛ[p]W1.T1 ➡*[h,n] ⓓ[p]ⓝW2.V2.T2.
 #h #n #G #L #V1 #V2 #HV12 #W1 #T1 #T2 #HT12 #W2 #H @(cprs_ind_dx … H) -W2
 [ /2 width=1 by cpms_beta_dx/
 | #W #W2 #_ #HW2 #IH #p >(plus_n_O … n) -HT12
@@ -60,10 +60,10 @@ qed.
 
 (* Basic_2A1: includes: cprs_beta *)
 theorem cpms_beta (h) (n) (G) (L):
-                  â\88\80W1,T1,T2. â\9dªG,L.â\93\9bW1â\9d« ⊢ T1 ➡*[h,n] T2 →
-                  â\88\80W2. â\9dªG,Lâ\9d« ⊢ W1 ➡*[h,0] W2 →
-                  â\88\80V1,V2. â\9dªG,Lâ\9d« ⊢ V1 ➡*[h,0] V2 →
-                  â\88\80p. â\9dªG,Lâ\9d« ⊢ ⓐV1.ⓛ[p]W1.T1 ➡*[h,n] ⓓ[p]ⓝW2.V2.T2.
+                  â\88\80W1,T1,T2. â\9d¨G,L.â\93\9bW1â\9d© ⊢ T1 ➡*[h,n] T2 →
+                  â\88\80W2. â\9d¨G,Lâ\9d© ⊢ W1 ➡*[h,0] W2 →
+                  â\88\80V1,V2. â\9d¨G,Lâ\9d© ⊢ V1 ➡*[h,0] V2 →
+                  â\88\80p. â\9d¨G,Lâ\9d© ⊢ ⓐV1.ⓛ[p]W1.T1 ➡*[h,n] ⓓ[p]ⓝW2.V2.T2.
 #h #n #G #L #W1 #T1 #T2 #HT12 #W2 #HW12 #V1 #V2 #H @(cprs_ind_dx … H) -V2
 [ /2 width=1 by cpms_beta_rc/
 | #V #V2 #_ #HV2 #IH #p >(plus_n_O … n) -HT12
@@ -73,10 +73,10 @@ qed.
 
 (* Basic_2A1: includes: cprs_theta_rc *)
 theorem cpms_theta_rc (h) (n) (G) (L):
-                      â\88\80V1,V. â\9dªG,Lâ\9d« ⊢ V1 ➡[h,0] V → ∀V2. ⇧[1] V ≘ V2 →
-                      â\88\80W1,T1,T2. â\9dªG,L.â\93\93W1â\9d« ⊢ T1 ➡*[h,n] T2 →
-                      â\88\80W2. â\9dªG,Lâ\9d« ⊢ W1 ➡*[h,0] W2 →
-                      â\88\80p. â\9dªG,Lâ\9d« ⊢ ⓐV1.ⓓ[p]W1.T1 ➡*[h,n] ⓓ[p]W2.ⓐV2.T2.
+                      â\88\80V1,V. â\9d¨G,Lâ\9d© ⊢ V1 ➡[h,0] V → ∀V2. ⇧[1] V ≘ V2 →
+                      â\88\80W1,T1,T2. â\9d¨G,L.â\93\93W1â\9d© ⊢ T1 ➡*[h,n] T2 →
+                      â\88\80W2. â\9d¨G,Lâ\9d© ⊢ W1 ➡*[h,0] W2 →
+                      â\88\80p. â\9d¨G,Lâ\9d© ⊢ ⓐV1.ⓓ[p]W1.T1 ➡*[h,n] ⓓ[p]W2.ⓐV2.T2.
 #h #n #G #L #V1 #V #HV1 #V2 #HV2 #W1 #T1 #T2 #HT12 #W2 #H @(cprs_ind_dx … H) -W2
 [ /2 width=3 by cpms_theta_dx/
 | #W #W2 #_ #HW2 #IH #p >(plus_n_O … n) -HT12
@@ -86,10 +86,10 @@ qed.
 
 (* Basic_2A1: includes: cprs_theta *)
 theorem cpms_theta (h) (n) (G) (L):
-                   â\88\80V,V2. â\87§[1] V â\89\98 V2 â\86\92 â\88\80W1,W2. â\9dªG,Lâ\9d« ⊢ W1 ➡*[h,0] W2 →
-                   â\88\80T1,T2. â\9dªG,L.â\93\93W1â\9d« ⊢ T1 ➡*[h,n] T2 →
-                   â\88\80V1. â\9dªG,Lâ\9d« ⊢ V1 ➡*[h,0] V →
-                   â\88\80p. â\9dªG,Lâ\9d« ⊢ ⓐV1.ⓓ[p]W1.T1 ➡*[h,n] ⓓ[p]W2.ⓐV2.T2.
+                   â\88\80V,V2. â\87§[1] V â\89\98 V2 â\86\92 â\88\80W1,W2. â\9d¨G,Lâ\9d© ⊢ W1 ➡*[h,0] W2 →
+                   â\88\80T1,T2. â\9d¨G,L.â\93\93W1â\9d© ⊢ T1 ➡*[h,n] T2 →
+                   â\88\80V1. â\9d¨G,Lâ\9d© ⊢ V1 ➡*[h,0] V →
+                   â\88\80p. â\9d¨G,Lâ\9d© ⊢ ⓐV1.ⓓ[p]W1.T1 ➡*[h,n] ⓓ[p]W2.ⓐV2.T2.
 #h #n #G #L #V #V2 #HV2 #W1 #W2 #HW12 #T1 #T2 #HT12 #V1 #H @(cprs_ind_sn … H) -V1
 [ /2 width=3 by cpms_theta_rc/
 | #V1 #V0 #HV10 #_ #IH #p >(plus_O_n … n) -HT12
@@ -99,24 +99,24 @@ qed.
 
 (* Basic_2A1: uses: lstas_scpds_trans scpds_strap2 *)
 theorem cpms_trans (h) (G) (L):
-        â\88\80n1,T1,T. â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,n1] T →
-        â\88\80n2,T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[h,n2] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,n1+n2] T2.
+        â\88\80n1,T1,T. â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,n1] T →
+        â\88\80n2,T2. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡*[h,n2] T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,n1+n2] T2.
 /2 width=3 by ltc_trans/ qed-.
 
 (* Basic_2A1: uses: scpds_cprs_trans *)
 theorem cpms_cprs_trans (h) (n) (G) (L):
-                        â\88\80T1,T. â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,n] T →
-                        â\88\80T2. â\9dªG,Lâ\9d« â\8a¢ T â\9e¡*[h,0] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,n] T2.
+                        â\88\80T1,T. â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,n] T →
+                        â\88\80T2. â\9d¨G,Lâ\9d© â\8a¢ T â\9e¡*[h,0] T2 â\86\92 â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,n] T2.
 #h #n #G #L #T1 #T #HT1 #T2 #HT2 >(plus_n_O … n)
 /2 width=3 by cpms_trans/ qed-.
 
 (* Advanced inversion lemmas ************************************************)
 
 lemma cpms_inv_appl_sn (h) (n) (G) (L):
-      â\88\80V1,T1,X2. â\9dªG,Lâ\9d« ⊢ ⓐV1.T1 ➡*[h,n] X2 →
-      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡*[h,0] V2 & â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,n] T2 & X2 = ⓐV2.T2
-       | â\88\83â\88\83n1,n2,p,W,T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h,n1] â\93\9b[p]W.T & â\9dªG,Lâ\9d« ⊢ ⓓ[p]ⓝW.V1.T ➡*[h,n2] X2 & n1 + n2 = n
-       | â\88\83â\88\83n1,n2,p,V0,V2,V,T. â\9dªG,Lâ\9d« â\8a¢ V1 â\9e¡*[h,0] V0 & â\87§[1] V0 â\89\98 V2 & â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h,n1] â\93\93[p]V.T & â\9dªG,Lâ\9d« ⊢ ⓓ[p]V.ⓐV2.T ➡*[h,n2] X2 & n1 + n2 = n.
+      â\88\80V1,T1,X2. â\9d¨G,Lâ\9d© ⊢ ⓐV1.T1 ➡*[h,n] X2 →
+      â\88¨â\88¨ â\88\83â\88\83V2,T2. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡*[h,0] V2 & â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,n] T2 & X2 = ⓐV2.T2
+       | â\88\83â\88\83n1,n2,p,W,T. â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡*[h,n1] â\93\9b[p]W.T & â\9d¨G,Lâ\9d© ⊢ ⓓ[p]ⓝW.V1.T ➡*[h,n2] X2 & n1 + n2 = n
+       | â\88\83â\88\83n1,n2,p,V0,V2,V,T. â\9d¨G,Lâ\9d© â\8a¢ V1 â\9e¡*[h,0] V0 & â\87§[1] V0 â\89\98 V2 & â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡*[h,n1] â\93\93[p]V.T & â\9d¨G,Lâ\9d© ⊢ ⓓ[p]V.ⓐV2.T ➡*[h,n2] X2 & n1 + n2 = n.
 #h #n #G #L #V1 #T1 #U2 #H
 @(cpms_ind_dx … H) -U2 /3 width=5 by or3_intro0, ex3_2_intro/
 #n1 #n2 #U #U2 #_ * *
@@ -140,8 +140,8 @@ lemma cpms_inv_appl_sn (h) (n) (G) (L):
 qed-.
 
 lemma cpms_inv_plus (h) (G) (L):
-      â\88\80n1,n2,T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,n1+n2] T2 →
-      â\88\83â\88\83T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h,n1] T & â\9dªG,Lâ\9d« ⊢ T ➡*[h,n2] T2.
+      â\88\80n1,n2,T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,n1+n2] T2 →
+      â\88\83â\88\83T. â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡*[h,n1] T & â\9d¨G,Lâ\9d© ⊢ T ➡*[h,n2] T2.
 #h #G #L #n1 elim n1 -n1 /2 width=3 by ex2_intro/
 #n1 #IH #n2 #T1 #T2 <plus_S1 #H
 elim (cpms_inv_succ_sn … H) -H #T0 #HT10 #HT02
@@ -153,9 +153,9 @@ qed-.
 (* Advanced main properties *************************************************)
 
 theorem cpms_cast (h) (n) (G) (L):
-        â\88\80T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ➡*[h,n] T2 →
-        â\88\80U1,U2. â\9dªG,Lâ\9d« ⊢ U1 ➡*[h,n] U2 →
-        â\9dªG,Lâ\9d« ⊢ ⓝU1.T1 ➡*[h,n] ⓝU2.T2.
+        â\88\80T1,T2. â\9d¨G,Lâ\9d© ⊢ T1 ➡*[h,n] T2 →
+        â\88\80U1,U2. â\9d¨G,Lâ\9d© ⊢ U1 ➡*[h,n] U2 →
+        â\9d¨G,Lâ\9d© ⊢ ⓝU1.T1 ➡*[h,n] ⓝU2.T2.
 #h #n #G #L #T1 #T2 #H @(cpms_ind_sn … H) -T1 -n
 [ /3 width=3 by cpms_cast_sn/
 | #n1 #n2 #T1 #T #HT1 #_ #IH #U1 #U2 #H
@@ -165,8 +165,8 @@ theorem cpms_cast (h) (n) (G) (L):
 qed.
 
 theorem cpms_trans_swap (h) (G) (L) (T1):
-        â\88\80n1,T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h,n1] T â\86\92 â\88\80n2,T2. â\9dªG,Lâ\9d« ⊢ T ➡*[h,n2] T2 →
-        â\88\83â\88\83T0. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡*[h,n2] T0 & â\9dªG,Lâ\9d« ⊢ T0 ➡*[h,n1] T2.
+        â\88\80n1,T. â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡*[h,n1] T â\86\92 â\88\80n2,T2. â\9d¨G,Lâ\9d© ⊢ T ➡*[h,n2] T2 →
+        â\88\83â\88\83T0. â\9d¨G,Lâ\9d© â\8a¢ T1 â\9e¡*[h,n2] T0 & â\9d¨G,Lâ\9d© ⊢ T0 ➡*[h,n1] T2.
 #h #G #L #T1 #n1 #T #HT1 #n2 #T2 #HT2
 lapply (cpms_trans … HT1 … HT2) -T <commutative_plus #HT12
 /2 width=1 by cpms_inv_plus/