update in basic_2

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_cprs.ma
index fe6b36fcd2ef2edb7be9cac9ee64e9547db062cf..990051c3a4039a08351e6cbfcaf7a4812a5c75c1 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_cprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cprs_cprs.ma
@@ -12,22 +12,29 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/rt_transition/lpr_lpr.ma".
 include "basic_2/rt_computation/cpms_cpms.ma".
+include "basic_2/rt_computation/cprs_cpr.ma".
 
-(* CONTEXT-SENSITIVE PARALLEL COMPUTATION FOR TERMS *************************)
+(* CONTEXT-SENSITIVE PARALLEL R-COMPUTATION FOR TERMS ***********************)
 
 (* Main properties **********************************************************)
 
 (* Basic_1: was: pr3_t *)
 (* Basic_1: includes: pr1_t *)
-theorem cprs_trans: ∀G,L. Transitive … (cprs G L).
-normalize /2 width=3 by trans_TC/ qed-.
+theorem cprs_trans (h) (G) (L): Transitive … (cpms h G L 0).
+/2 width=3 by cpms_trans/ qed-.
 
 (* Basic_1: was: pr3_confluence *)
 (* Basic_1: includes: pr1_confluence *)
-theorem cprs_conf: ∀G,L. confluent2 … (cprs G L) (cprs G L).
-normalize /3 width=3 by cpr_conf, TC_confluent2/ qed-.
+theorem cprs_conf (h) (G) (L): confluent2 … (cpms h G L 0) (cpms h G L 0).
+#h #G #L #T0 #T1 #HT01 #T2 #HT02
+elim (TC_confluent2 … T0 T1 … T2)
+[ /3 width=3 by cprs_CTC, ex2_intro/ |5,6: skip
+| /2 width=1 by cprs_inv_CTC/
+| /2 width=1 by cprs_inv_CTC/
+| /2 width=3 by cpr_conf/
+]
+qed-.
 
 (* Basic_1: was: pr3_flat *)
 theorem cprs_flat (h) (G) (L):
@@ -43,48 +50,24 @@ qed.
 (* Advanced inversion lemmas ************************************************)
 
 (* Basic_1: was pr3_gen_appl *)
-lemma cprs_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
-                       | ∃∃a,W,T.       ⦃G, L⦄ ⊢ T1 ➡* ⓛ{a}W.T &
-                                        ⦃G, L⦄ ⊢ ⓓ{a}ⓝW.V1.T ➡* U2
-                       | ∃∃a,V0,V2,V,T. ⦃G, L⦄ ⊢ V1 ➡* V0 & ⬆[0,1] V0 ≘ V2 &
-                                        ⦃G, L⦄ ⊢ T1 ➡* ⓓ{a}V.T &
-                                        ⦃G, L⦄ ⊢ ⓓ{a}V.ⓐV2.T ➡* U2.
-#G #L #V1 #T1 #U2 #H @(cprs_ind … H) -U2 /3 width=5 by or3_intro0, ex3_2_intro/
-#U #U2 #_ #HU2 * *
-[ #V0 #T0 #HV10 #HT10 #H destruct
-  elim (cpr_inv_appl1 … HU2) -HU2 *
-  [ #V2 #T2 #HV02 #HT02 #H destruct /4 width=5 by cprs_strap1, or3_intro0, ex3_2_intro/
-  | #a #V2 #W #W2 #T #T2 #HV02 #HW2 #HT2 #H1 #H2 destruct
-    lapply (cprs_strap1 … HV10 … HV02) -V0 #HV12
-    lapply (lsubr_cpr_trans … HT2 (L.ⓓⓝW.V1) ?) -HT2
-    /5 width=5 by cprs_bind, cprs_flat_dx, cpr_cprs, lsubr_beta, ex2_3_intro, or3_intro1/
-  | #a #V #V2 #W0 #W2 #T #T2 #HV0 #HV2 #HW02 #HT2 #H1 #H2 destruct
-    /5 width=10 by cprs_flat_sn, cprs_bind_dx, cprs_strap1, ex4_5_intro, or3_intro2/
-  ]
-| /4 width=9 by cprs_strap1, or3_intro1, ex2_3_intro/
-| /4 width=11 by cprs_strap1, or3_intro2, ex4_5_intro/
+(* Basic_2A1: was: cprs_inv_appl1 *)
+lemma cprs_inv_appl_sn (h) (G) (L):
+                       ∀V1,T1,X2. ⦃G, L⦄ ⊢ ⓐV1.T1 ➡*[h] X2 →
+                       ∨∨ ∃∃V2,T2.       ⦃G, L⦄ ⊢ V1 ➡*[h] V2 &
+                                         ⦃G, L⦄ ⊢ T1 ➡*[h] T2 &
+                                         X2 = ⓐV2. T2
+                        | ∃∃p,W,T.       ⦃G, L⦄ ⊢ T1 ➡*[h] ⓛ{p}W.T &
+                                         ⦃G, L⦄ ⊢ ⓓ{p}ⓝW.V1.T ➡*[h] X2
+                        | ∃∃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] X2.
+#h #G #L #V1 #T1 #X2 #H elim (cpms_inv_appl_sn … H) -H *
+[ /3 width=5 by or3_intro0, ex3_2_intro/
+| #n1 #n2 #p #V2 #T2 #HT12 #HTX2 #H
+  elim (plus_inv_O3 … H) -H #H1 #H2 destruct
+  /3 width=5 by or3_intro1, ex2_3_intro/
+| #n1 #n2 #p #V2 #W2 #V #T2 #HV12 #HVW2 #HT12 #HTX2 #H
+  elim (plus_inv_O3 … H) -H #H1 #H2 destruct
+  /3 width=9 by or3_intro2, ex4_5_intro/
 ]
 qed-.
-
-(* Basic_1: was: pr3_strip *)
-(* Basic_1: includes: pr1_strip *)
-lemma cprs_strip: ∀G,L. confluent2 … (cprs G L) (cpr G L).
-normalize /4 width=3 by cpr_conf, TC_strip1/ qed-.
-
-lemma cprs_lpr_conf_dx: ∀G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ➡* T1 → ∀L1. ⦃G, L0⦄ ⊢ ➡ L1 →
-                        ∃∃T. ⦃G, L1⦄ ⊢ T1 ➡* T & ⦃G, L1⦄ ⊢ T0 ➡* T.
-#G #L0 #T0 #T1 #H @(cprs_ind … H) -T1 /2 width=3 by ex2_intro/
-#T #T1 #_ #HT1 #IHT0 #L1 #HL01 elim (IHT0 … HL01)
-#T2 #HT2 #HT02 elim (lpr_cpr_conf_dx … HT1 … HL01) -L0
-#T3 #HT3 #HT13 elim (cprs_strip … HT2 … HT3) -T
-/4 width=5 by cprs_strap2, cprs_strap1, ex2_intro/
-qed-.
-
-lemma cprs_lpr_conf_sn: ∀G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ➡* T1 →
-                        ∀L1. ⦃G, L0⦄ ⊢ ➡ L1 →
-                        ∃∃T. ⦃G, L0⦄ ⊢ T1 ➡* T & ⦃G, L1⦄ ⊢ T0 ➡* T.
-#G #L0 #T0 #T1 #HT01 #L1 #HL01 elim (cprs_lpr_conf_dx … HT01 … HL01) -HT01
-/3 width=3 by lpr_cprs_trans, ex2_intro/
-qed-.