update in ground_2, static_2, basic_2, apps_2, alpha_1

[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 e2347a29621293225bd1d7958a79cd4f76cf2ebd..5ab4a39153cddbe148eedb432f0a76be4053950a 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
@@ -23,58 +23,58 @@ include "basic_2/rt_computation/cpxs.ma".
 theorem cpxs_trans: ∀h,G,L. Transitive … (cpxs h G L).
 normalize /2 width=3 by trans_TC/ qed-.
 
-theorem cpxs_bind: â\88\80h,p,I,G,L,V1,V2,T1,T2. â¦\83G,L.â\93\91{I}V1â¦\84 ⊢ T1 ⬈*[h] T2 →
-                   â¦\83G,Lâ¦\84 ⊢ V1 ⬈*[h] V2 →
-                   â¦\83G,Lâ¦\84 â\8a¢ â\93\91{p,I}V1.T1 â¬\88*[h] â\93\91{p,I}V2.T2.
+theorem cpxs_bind: â\88\80h,p,I,G,L,V1,V2,T1,T2. â\9dªG,L.â\93\91[I]V1â\9d« ⊢ T1 ⬈*[h] T2 →
+                   â\9dªG,Lâ\9d« ⊢ V1 ⬈*[h] V2 →
+                   â\9dªG,Lâ\9d« â\8a¢ â\93\91[p,I]V1.T1 â¬\88*[h] â\93\91[p,I]V2.T2.
 #h #p #I #G #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2
 /3 width=5 by cpxs_trans, cpxs_bind_dx/
 qed.
 
-theorem cpxs_flat: â\88\80h,I,G,L,V1,V2,T1,T2. â¦\83G,Lâ¦\84 ⊢ T1 ⬈*[h] T2 →
-                   â¦\83G,Lâ¦\84 ⊢ V1 ⬈*[h] V2 →
-                   â¦\83G,Lâ¦\84 â\8a¢ â\93\95{I}V1.T1 â¬\88*[h] â\93\95{I}V2.T2.
+theorem cpxs_flat: â\88\80h,I,G,L,V1,V2,T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ⬈*[h] T2 →
+                   â\9dªG,Lâ\9d« ⊢ V1 ⬈*[h] V2 →
+                   â\9dªG,Lâ\9d« â\8a¢ â\93\95[I]V1.T1 â¬\88*[h] â\93\95[I]V2.T2.
 #h #I #G #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2
 /3 width=5 by cpxs_trans, cpxs_flat_dx/
 qed.
 
 theorem cpxs_beta_rc: ∀h,p,G,L,V1,V2,W1,W2,T1,T2.
-                      â¦\83G,Lâ¦\84 â\8a¢ V1 â¬\88[h] V2 â\86\92 â¦\83G,L.â\93\9bW1â¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ W1 ⬈*[h] W2 →
-                      â¦\83G,Lâ¦\84 â\8a¢ â\93\90V1.â\93\9b{p}W1.T1 â¬\88*[h] â\93\93{p}ⓝW2.V2.T2.
+                      â\9dªG,Lâ\9d« â\8a¢ V1 â¬\88[h] V2 â\86\92 â\9dªG,L.â\93\9bW1â\9d« â\8a¢ T1 â¬\88*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ W1 ⬈*[h] W2 →
+                      â\9dªG,Lâ\9d« â\8a¢ â\93\90V1.â\93\9b[p]W1.T1 â¬\88*[h] â\93\93[p]ⓝW2.V2.T2.
 #h #p #G #L #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: ∀h,p,G,L,V1,V2,W1,W2,T1,T2.
-                   â¦\83G,L.â\93\9bW1â¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 â¦\83G,Lâ¦\84 â\8a¢ W1 â¬\88*[h] W2 â\86\92 â¦\83G,Lâ¦\84 ⊢ V1 ⬈*[h] V2 →
-                   â¦\83G,Lâ¦\84 â\8a¢ â\93\90V1.â\93\9b{p}W1.T1 â¬\88*[h] â\93\93{p}ⓝW2.V2.T2.
+                   â\9dªG,L.â\93\9bW1â\9d« â\8a¢ T1 â¬\88*[h] T2 â\86\92 â\9dªG,Lâ\9d« â\8a¢ W1 â¬\88*[h] W2 â\86\92 â\9dªG,Lâ\9d« ⊢ V1 ⬈*[h] V2 →
+                   â\9dªG,Lâ\9d« â\8a¢ â\93\90V1.â\93\9b[p]W1.T1 â¬\88*[h] â\93\93[p]ⓝW2.V2.T2.
 #h #p #G #L #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: ∀h,p,G,L,V1,V,V2,W1,W2,T1,T2.
-                       â¦\83G,Lâ¦\84 ⊢ V1 ⬈[h] V → ⇧*[1] V ≘ V2 →
-                       â¦\83G,L.â\93\93W1â¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ W1 ⬈*[h] W2 →
-                       â¦\83G,Lâ¦\84 â\8a¢ â\93\90V1.â\93\93{p}W1.T1 â¬\88*[h] â\93\93{p}W2.ⓐV2.T2.
+                       â\9dªG,Lâ\9d« ⊢ V1 ⬈[h] V → ⇧*[1] V ≘ V2 →
+                       â\9dªG,L.â\93\93W1â\9d« â\8a¢ T1 â¬\88*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ W1 ⬈*[h] W2 →
+                       â\9dªG,Lâ\9d« â\8a¢ â\93\90V1.â\93\93[p]W1.T1 â¬\88*[h] â\93\93[p]W2.ⓐV2.T2.
 #h #p #G #L #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: ∀h,p,G,L,V1,V,V2,W1,W2,T1,T2.
-                    â\87§*[1] V â\89\98 V2 â\86\92 â¦\83G,Lâ¦\84 ⊢ W1 ⬈*[h] W2 →
-                    â¦\83G,L.â\93\93W1â¦\84 â\8a¢ T1 â¬\88*[h] T2 â\86\92 â¦\83G,Lâ¦\84 ⊢ V1 ⬈*[h] V →
-                    â¦\83G,Lâ¦\84 â\8a¢ â\93\90V1.â\93\93{p}W1.T1 â¬\88*[h] â\93\93{p}W2.ⓐV2.T2.
+                    â\87§*[1] V â\89\98 V2 â\86\92 â\9dªG,Lâ\9d« ⊢ W1 ⬈*[h] W2 →
+                    â\9dªG,L.â\93\93W1â\9d« â\8a¢ T1 â¬\88*[h] T2 â\86\92 â\9dªG,Lâ\9d« ⊢ V1 ⬈*[h] V →
+                    â\9dªG,Lâ\9d« â\8a¢ â\93\90V1.â\93\93[p]W1.T1 â¬\88*[h] â\93\93[p]W2.ⓐV2.T2.
 #h #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.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpxs_inv_appl1: â\88\80h,G,L,V1,T1,U2. â¦\83G,Lâ¦\84 ⊢ ⓐV1.T1 ⬈*[h] U2 →
-                      â\88¨â\88¨ â\88\83â\88\83V2,T2.       â¦\83G,Lâ¦\84 â\8a¢ V1 â¬\88*[h] V2 & â¦\83G,Lâ¦\84 ⊢ T1 ⬈*[h] T2 &
+lemma cpxs_inv_appl1: â\88\80h,G,L,V1,T1,U2. â\9dªG,Lâ\9d« ⊢ ⓐV1.T1 ⬈*[h] U2 →
+                      â\88¨â\88¨ â\88\83â\88\83V2,T2.       â\9dªG,Lâ\9d« â\8a¢ V1 â¬\88*[h] V2 & â\9dªG,Lâ\9d« ⊢ T1 ⬈*[h] T2 &
                                         U2 = ⓐV2.T2
-                       | â\88\83â\88\83p,W,T.       â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\88*[h] â\93\9b{p}W.T & â¦\83G,Lâ¦\84 â\8a¢ â\93\93{p}ⓝW.V1.T ⬈*[h] U2
-                       | â\88\83â\88\83p,V0,V2,V,T. â¦\83G,Lâ¦\84 ⊢ V1 ⬈*[h] V0 & ⇧*[1] V0 ≘ V2 &
-                                        â¦\83G,Lâ¦\84 â\8a¢ T1 â¬\88*[h] â\93\93{p}V.T & â¦\83G,Lâ¦\84 â\8a¢ â\93\93{p}V.ⓐV2.T ⬈*[h] U2.
+                       | â\88\83â\88\83p,W,T.       â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88*[h] â\93\9b[p]W.T & â\9dªG,Lâ\9d« â\8a¢ â\93\93[p]ⓝW.V1.T ⬈*[h] U2
+                       | â\88\83â\88\83p,V0,V2,V,T. â\9dªG,Lâ\9d« ⊢ V1 ⬈*[h] V0 & ⇧*[1] V0 ≘ V2 &
+                                        â\9dªG,Lâ\9d« â\8a¢ T1 â¬\88*[h] â\93\93[p]V.T & â\9dªG,Lâ\9d« â\8a¢ â\93\93[p]V.ⓐV2.T ⬈*[h] U2.
 #h #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