commit completed: now we support two versions of slicing for local

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / computation / cpxs_cpys.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpys.ma b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpys.ma
index 0bbe9835cf4d98570f743bd2b3f9cc06ee3b15bf..7ab36e5be0595617575333d989766d0e75b1fb34 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpys.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/computation/cpxs_cpys.ma
@@ -13,23 +13,40 @@
 (**************************************************************************)
 
 include "basic_2/substitution/cpys_cpys.ma".
+include "basic_2/reduction/cpx_cpys.ma".
 include "basic_2/computation/cpxs_cpxs.ma".
 
 (* SN EXTENDED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS ********************)
 
 (* Main properties **********************************************************)
 
-lemma cpx_fwd_cpys_tpxs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 →
+axiom cpys_split_down: ∀G,L,T1,T2,d,e. ⦃G, L⦄ ⊢ T1 ▶*×[d, e] T2 →
+                       ∀i. d ≤ i → i ≤ d + e →
+                       ∃∃T. ⦃G, L⦄ ⊢ T1 ▶*×[i, d+e-i] T & ⦃G, L⦄ ⊢ T ▶*×[d, i-d] T2.
+
+lemma cpys_tpxs_trans: ∀h,g,G,L,T1,T,d,e. ⦃G, L⦄ ⊢ T1 ▶*×[d, e] T →
+                       ∀T2. ⦃G, ⋆⦄ ⊢ T ➡*[h, g] T2 → ⦃G, L⦄ ⊢ T1 ➡*[h, g] T2.
+#h #g #G #L #T1 #T #d #e #HT1 #T2 #H @(cpxs_ind … H) -T2
+/3 width=5 by cpxs_strap1, cpys_cpx, lsubr_cpx_trans, cpx_cpxs/
+qed-.
+
+axiom cpx_fwd_cpys_tpxs: ∀h,g,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[h, g] T2 →
                          ∃∃T. ⦃G, L⦄ ⊢ T1 ▶*×[0, ∞] T & ⦃G, ⋆⦄ ⊢ T ➡*[h, g] T2.
+(*
 #h #g #G #L #T1 #T2 #H elim H -G -L -T1 -T2
 [ /2 width=3 by ex2_intro/
 | /4 width=3 by cpx_cpxs, cpx_sort, ex2_intro/
 | #I #G #L #K #V1 #V2 #W2 #i #HLK #_ #HVW2 * #V #HV1 #HV2
   elim (lift_total V 0 (i+1)) #W #HVW
-  @(ex2_intro … W) /2 width=7 by cpys_subst_Y2/
+  lapply (cpxs_lift … HV2 (⋆) (Ⓣ) … HVW … HVW2)
+  [ @ldrop_atom #H destruct | /3 width=7 by cpys_subst_Y2, ex2_intro/ ]
 | #a #I #G #L #V1 #V2 #T1 #T2 #_ #_ * #V #HV1 #HV2 * #T #HT1 #HT2
-  elim (cpys_split_up … HT1 1) -HT1 // #T0 #HT10 #HT0
+  elim (cpys_split_down … HT1 1) -HT1 // #T0 #HT10 #HT0 
+(*  
   @(ex2_intro … (ⓑ{a,I}V.T0))
-  [ @(cpys_bind … HV1) -HV1
+  [ @cpys_bind // 
   | @(cpxs_bind … HV2) -HV2
-  ]  
+  
+  /2 width=5 by cpys_tpxs_trans/
+  ]
+*)*)
\ No newline at end of file