X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frt_computation%2Fcpxs_cpxs.ma;h=92146c7eeb0e3abee1e10afb5bf90dff45e5aeff;hb=3c7b4071a9ac096b02334c1d47468776b948e2de;hp=60ddf6394ca9621351724650c5f18c663e286940;hpb=db020b4218272e2e35641ce3bc3b0a9b3afda899;p=helm.git

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 60ddf6394..92146c7ee 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_cpxs.ma
@@ -12,69 +12,76 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "ground/xoa/ex_4_5.ma".
 include "basic_2/rt_transition/cpx_lsubr.ma".
 include "basic_2/rt_computation/cpxs.ma".
 
-(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
+(* EXTENDED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS *************)
 
 (* Main properties **********************************************************)
 
-theorem cpxs_trans: ∀h,G,L. Transitive … (cpxs h G L).
+theorem cpxs_trans (G) (L):
+        Transitive … (cpxs G L).
 normalize /2 width=3 by trans_TC/ qed-.
 
-theorem cpxs_bind: ∀h,p,I,G,L,V1,V2,T1,T2. ⦃G,L.ⓑ{I}V1⦄ ⊢ T1 ⬈*[h] T2 →
-                   ⦃G,L⦄ ⊢ V1 ⬈*[h] V2 →
-                   ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈*[h] ⓑ{p,I}V2.T2.
-#h #p #I #G #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2
+theorem cpxs_bind (G) (L):
+        ∀p,I,V1,V2,T1,T2. ❪G,L.ⓑ[I]V1❫ ⊢ T1 ⬈* T2 →
+        ❪G,L❫ ⊢ V1 ⬈* V2 →
+        ❪G,L❫ ⊢ ⓑ[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: ∀h,I,G,L,V1,V2,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 →
-                   ⦃G,L⦄ ⊢ V1 ⬈*[h] V2 →
-                   ⦃G,L⦄ ⊢ ⓕ{I}V1.T1 ⬈*[h] ⓕ{I}V2.T2.
-#h #I #G #L #V1 #V2 #T1 #T2 #HT12 #H @(cpxs_ind … H) -V2
+theorem cpxs_flat (G) (L):
+        ∀I,V1,V2,T1,T2. ❪G,L❫ ⊢ T1 ⬈* T2 →
+        ❪G,L❫ ⊢ V1 ⬈* V2 →
+        ❪G,L❫ ⊢ ⓕ[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: ∀h,p,G,L,V1,V2,W1,W2,T1,T2.
-                      ⦃G,L⦄ ⊢ V1 ⬈[h] V2 → ⦃G,L.ⓛW1⦄ ⊢ T1 ⬈*[h] T2 → ⦃G,L⦄ ⊢ W1 ⬈*[h] W2 →
-                      ⦃G,L⦄ ⊢ ⓐV1.ⓛ{p}W1.T1 ⬈*[h] ⓓ{p}ⓝW2.V2.T2.
-#h #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HT12 #H @(cpxs_ind … H) -W2
+theorem cpxs_beta_rc (G) (L):
+        ∀p,V1,V2,W1,W2,T1,T2.
+        ❪G,L❫ ⊢ V1 ⬈ V2 → ❪G,L.ⓛW1❫ ⊢ T1 ⬈* T2 → ❪G,L❫ ⊢ W1 ⬈* W2 →
+        ❪G,L❫ ⊢ ⓐ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: ∀h,p,G,L,V1,V2,W1,W2,T1,T2.
-                   ⦃G,L.ⓛW1⦄ ⊢ T1 ⬈*[h] T2 → ⦃G,L⦄ ⊢ W1 ⬈*[h] W2 → ⦃G,L⦄ ⊢ V1 ⬈*[h] V2 →
-                   ⦃G,L⦄ ⊢ ⓐV1.ⓛ{p}W1.T1 ⬈*[h] ⓓ{p}ⓝW2.V2.T2.
-#h #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HT12 #HW12 #H @(cpxs_ind … H) -V2
+theorem cpxs_beta (G) (L):
+        ∀p,V1,V2,W1,W2,T1,T2.
+        ❪G,L.ⓛW1❫ ⊢ T1 ⬈* T2 → ❪G,L❫ ⊢ W1 ⬈* W2 → ❪G,L❫ ⊢ V1 ⬈* V2 →
+        ❪G,L❫ ⊢ ⓐ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: ∀h,p,G,L,V1,V,V2,W1,W2,T1,T2.
-                       ⦃G,L⦄ ⊢ V1 ⬈[h] V → ⬆*[1] V ≘ V2 →
-                       ⦃G,L.ⓓW1⦄ ⊢ T1 ⬈*[h] T2 → ⦃G,L⦄ ⊢ W1 ⬈*[h] W2 →
-                       ⦃G,L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ⬈*[h] ⓓ{p}W2.ⓐV2.T2.
-#h #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 #HT12 #H @(cpxs_ind … H) -W2
+theorem cpxs_theta_rc (G) (L):
+        ∀p,V1,V,V2,W1,W2,T1,T2.
+        ❪G,L❫ ⊢ V1 ⬈ V → ⇧[1] V ≘ V2 →
+        ❪G,L.ⓓW1❫ ⊢ T1 ⬈* T2 → ❪G,L❫ ⊢ W1 ⬈* W2 →
+        ❪G,L❫ ⊢ ⓐ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: ∀h,p,G,L,V1,V,V2,W1,W2,T1,T2.
-                    ⬆*[1] V ≘ V2 → ⦃G,L⦄ ⊢ W1 ⬈*[h] W2 →
-                    ⦃G,L.ⓓW1⦄ ⊢ T1 ⬈*[h] T2 → ⦃G,L⦄ ⊢ V1 ⬈*[h] V →
-                    ⦃G,L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ⬈*[h] ⓓ{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
+theorem cpxs_theta (G) (L):
+        ∀p,V1,V,V2,W1,W2,T1,T2.
+        ⇧[1] V ≘ V2 → ❪G,L❫ ⊢ W1 ⬈* W2 →
+        ❪G,L.ⓓW1❫ ⊢ T1 ⬈* T2 → ❪G,L❫ ⊢ V1 ⬈* V →
+        ❪G,L❫ ⊢ ⓐ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.
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma cpxs_inv_appl1: ∀h,G,L,V1,T1,U2. ⦃G,L⦄ ⊢ ⓐV1.T1 ⬈*[h] U2 →
-                      ∨∨ ∃∃V2,T2.       ⦃G,L⦄ ⊢ V1 ⬈*[h] V2 & ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 &
-                                        U2 = ⓐV2.T2
-                       | ∃∃p,W,T.       ⦃G,L⦄ ⊢ T1 ⬈*[h] ⓛ{p}W.T & ⦃G,L⦄ ⊢ ⓓ{p}ⓝW.V1.T ⬈*[h] U2
-                       | ∃∃p,V0,V2,V,T. ⦃G,L⦄ ⊢ V1 ⬈*[h] V0 & ⬆*[1] V0 ≘ V2 &
-                                        ⦃G,L⦄ ⊢ T1 ⬈*[h] ⓓ{p}V.T & ⦃G,L⦄ ⊢ ⓓ{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/ ]
+lemma cpxs_inv_appl1 (G) (L):
+      ∀V1,T1,U2. ❪G,L❫ ⊢ ⓐV1.T1 ⬈* U2 →
+      ∨∨ ∃∃V2,T2. ❪G,L❫ ⊢ V1 ⬈* V2 & ❪G,L❫ ⊢ T1 ⬈* T2 & U2 = ⓐV2.T2
+       | ∃∃p,W,T. ❪G,L❫ ⊢ T1 ⬈* ⓛ[p]W.T & ❪G,L❫ ⊢ ⓓ[p]ⓝW.V1.T ⬈* U2
+       | ∃∃p,V0,V2,V,T. ❪G,L❫ ⊢ V1 ⬈* V0 & ⇧[1] V0 ≘ V2 & ❪G,L❫ ⊢ T1 ⬈* ⓓ[p]V.T & ❪G,L❫ ⊢ ⓓ[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
   elim (cpx_inv_appl1 … HU2) -HU2 *