- advances on lfxs for lfpxs

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tsts.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tsts.ma
index ace2532d977db9b6c33ce4b77466f96d66084bef..64f1facd20f1661a5f5cad00905a39bdc1f2d59c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tsts.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tsts.ma
@@ -12,39 +12,31 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/grammar/tsts.ma".
-include "basic_2/computation/lpxs_cpxs.ma".
+include "basic_2/syntax/tsts.ma".
+include "basic_2/rt_computation/lfpxs_cpxs.ma".
 
-(* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************)
+(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
 
-(* Forward lemmas involving same top term structure *************************)
-
-lemma cpxs_fwd_cnx: â\88\80h,o,G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â\9e¡[h, o] ð\9d\90\8dâ¦\83Tâ¦\84 â\86\92 â\88\80U. â¦\83G, Lâ¦\84 â\8a¢ T â\9e¡*[h, o] U → T ≂ U.
+(* Forward lemmas with same top term structure ******************************)
+(*
+lemma cpxs_fwd_cnx: â\88\80h,o,G,L,T. â¦\83G, Lâ¦\84 â\8a¢ â¬\88[h, o] ð\9d\90\8dâ¦\83Tâ¦\84 â\86\92 â\88\80U. â¦\83G, Lâ¦\84 â\8a¢ T â¬\88*[h, o] U → T ≂ U.
 #h #o #G #L #T #HT #U #H
 >(cpxs_inv_cnx1 … H HT) -G -L -T //
 qed-.
-
-lemma cpxs_fwd_sort: ∀h,o,G,L,U,s. ⦃G, L⦄ ⊢ ⋆s ➡*[h, o] U →
-                     ⋆s ≂ U ∨ ⦃G, L⦄ ⊢ ⋆(next h s) ➡*[h, o] U.
-#h #o #G #L #U #s #H
-elim (cpxs_inv_sort1 … H) -H #n #d generalize in match s; -s @(nat_ind_plus … n) -n
-[ #s #_ #H -d destruct /2 width=1 by or_introl/
-| #n #IHn #s >plus_plus_comm_23 #Hnd #H destruct
-  lapply (deg_next_SO … Hnd) -Hnd #Hnd
-  elim (IHn … Hnd) -IHn
-  [ #H lapply (tsts_inv_atom1 … H) -H #H >H -H /2 width=1 by or_intror/
-  | generalize in match Hnd; -Hnd @(nat_ind_plus … n) -n
-    /4 width=3 by cpxs_strap2, cpx_st, or_intror/
-  | >iter_SO >iter_n_Sm //
-  ]
+*)
+lemma cpxs_fwd_sort: ∀h,G,L,U,s. ⦃G, L⦄ ⊢ ⋆s ⬈*[h] U →
+                     ⋆s ≂ U ∨ ⦃G, L⦄ ⊢ ⋆(next h s) ⬈*[h] U.
+#h #G #L #U #s #H elim (cpxs_inv_sort1 … H) -H *
+[ #H destruct /2 width=1 by or_introl/
+| #n #H destruct
+  @or_intror >iter_S <(iter_n_Sm … (next h)) // (**)
 ]
 qed-.
 
 (* Basic_1: was just: pr3_iso_beta *)
-lemma cpxs_fwd_beta: ∀h,o,a,G,L,V,W,T,U. ⦃G, L⦄ ⊢ ⓐV.ⓛ{a}W.T ➡*[h, o] U →
-                     ⓐV.ⓛ{a}W.T ≂ U ∨ ⦃G, L⦄ ⊢ ⓓ{a}ⓝW.V.T ➡*[h, o] U.
-#h #o #a #G #L #V #W #T #U #H
-elim (cpxs_inv_appl1 … H) -H *
+lemma cpxs_fwd_beta: ∀h,p,G,L,V,W,T,U. ⦃G, L⦄ ⊢ ⓐV.ⓛ{p}W.T ⬈*[h] U →
+                     ⓐV.ⓛ{p}W.T ≂ U ∨ ⦃G, L⦄ ⊢ ⓓ{p}ⓝW.V.T ⬈*[h] U.
+#h #p #G #L #V #W #T #U #H elim (cpxs_inv_appl1 … H) -H *
 [ #V0 #T0 #_ #_ #H destruct /2 width=1 by tsts_pair, or_introl/
 | #b #W0 #T0 #HT0 #HU
   elim (cpxs_inv_abst1 … HT0) -HT0 #W1 #T1 #HW1 #HT1 #H destruct
@@ -58,8 +50,8 @@ qed-.
 (* Note: probably this is an inversion lemma *)
 lemma cpxs_fwd_delta: ∀h,o,I,G,L,K,V1,i. ⬇[i] L ≡ K.ⓑ{I}V1 →
                       ∀V2. ⬆[0, i + 1] V1 ≡ V2 →
-                      â\88\80U. â¦\83G, Lâ¦\84 â\8a¢ #i â\9e¡*[h, o] U →
-                      #i â\89\82 U â\88¨ â¦\83G, Lâ¦\84 â\8a¢ V2 â\9e¡*[h, o] U.
+                      â\88\80U. â¦\83G, Lâ¦\84 â\8a¢ #i â¬\88*[h, o] U →
+                      #i â\89\82 U â\88¨ â¦\83G, Lâ¦\84 â\8a¢ V2 â¬\88*[h, o] U.
 #h #o #I #G #L #K #V1 #i #HLK #V2 #HV12 #U #H
 elim (cpxs_inv_lref1 … H) -H /2 width=1 by or_introl/
 * #I0 #K0 #V0 #U0 #HLK0 #HVU0 #HU0
@@ -67,9 +59,9 @@ lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct
 /4 width=10 by cpxs_lift, drop_fwd_drop2, or_intror/
 qed-.
 
-lemma cpxs_fwd_theta: â\88\80h,o,a,G,L,V1,V,T,U. â¦\83G, Lâ¦\84 â\8a¢ â\93\90V1.â\93\93{a}V.T â\9e¡*[h, o] U →
+lemma cpxs_fwd_theta: â\88\80h,o,a,G,L,V1,V,T,U. â¦\83G, Lâ¦\84 â\8a¢ â\93\90V1.â\93\93{a}V.T â¬\88*[h, o] U →
                       ∀V2. ⬆[0, 1] V1 ≡ V2 → ⓐV1.ⓓ{a}V.T ≂ U ∨
-                      â¦\83G, Lâ¦\84 â\8a¢ â\93\93{a}V.â\93\90V2.T â\9e¡*[h, o] U.
+                      â¦\83G, Lâ¦\84 â\8a¢ â\93\93{a}V.â\93\90V2.T â¬\88*[h, o] U.
 #h #o #a #G #L #V1 #V #T #U #H #V2 #HV12
 elim (cpxs_inv_appl1 … H) -H *
 [ -HV12 #V0 #T0 #_ #_ #H destruct /2 width=1 by tsts_pair, or_introl/
@@ -99,8 +91,8 @@ elim (cpxs_inv_appl1 … H) -H *
 ]
 qed-.
 
-lemma cpxs_fwd_cast: â\88\80h,o,G,L,W,T,U. â¦\83G, Lâ¦\84 â\8a¢ â\93\9dW.T â\9e¡*[h, o] U →
-                     â\88¨â\88¨ â\93\9dW. T â\89\82 U | â¦\83G, Lâ¦\84 â\8a¢ T â\9e¡*[h, o] U | â¦\83G, Lâ¦\84 â\8a¢ W â\9e¡*[h, o] U.
+lemma cpxs_fwd_cast: â\88\80h,o,G,L,W,T,U. â¦\83G, Lâ¦\84 â\8a¢ â\93\9dW.T â¬\88*[h, o] U →
+                     â\88¨â\88¨ â\93\9dW. T â\89\82 U | â¦\83G, Lâ¦\84 â\8a¢ T â¬\88*[h, o] U | â¦\83G, Lâ¦\84 â\8a¢ W â¬\88*[h, o] U.
 #h #o #G #L #W #T #U #H
 elim (cpxs_inv_cast1 … H) -H /2 width=1 by or3_intro1, or3_intro2/ *
 #W0 #T0 #_ #_ #H destruct /2 width=1 by tsts_pair, or3_intro0/