- the PARTIAL COMMIT continues, we issue the "reduction" component

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / reduction / cpr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpr.ma b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpr.ma
index 7fcfa3f323aed2e9eecdcad047978d4a41f32d23..d2034f9d196d5f2e421b86d31102095990f4b0bb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/reduction/cpr.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/reduction/cpr.ma
@@ -14,9 +14,8 @@
 
 include "basic_2/notation/relations/pred_4.ma".
 include "basic_2/grammar/genv.ma".
-include "basic_2/grammar/cl_shift.ma".
-include "basic_2/relocation/ldrop_append.ma".
-include "basic_2/relocation/lsubr.ma".
+include "basic_2/static/lsubr.ma".
+include "basic_2/unfold/lstas.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS ***************************)
 
@@ -36,7 +35,7 @@ inductive cpr: relation4 genv lenv term term ≝
              cpr G L (ⓕ{I}V1.T1) (ⓕ{I}V2.T2)
 | cpr_zeta : ∀G,L,V,T1,T,T2. cpr G (L.ⓓV) T1 T →
              ⇧[0, 1] T2 ≡ T → cpr G L (+ⓓV.T1) T2
-| cpr_tau  : ∀G,L,V,T1,T2. cpr G L T1 T2 → cpr G L (ⓝV.T1) T2
+| cpr_eps  : ∀G,L,V,T1,T2. cpr G L T1 T2 → cpr G L (ⓝV.T1) T2
 | cpr_beta : ∀a,G,L,V1,V2,W1,W2,T1,T2.
              cpr G L V1 V2 → cpr G L W1 W2 → cpr G (L.ⓛW1) T1 T2 →
              cpr G L (ⓐV1.ⓛ{a}W1.T1) (ⓓ{a}ⓝW2.V2.T2)
@@ -54,11 +53,11 @@ lemma lsubr_cpr_trans: ∀G. lsub_trans … (cpr G) lsubr.
 #G #L1 #T1 #T2 #H elim H -G -L1 -T1 -T2
 [ //
 | #G #L1 #K1 #V1 #V2 #W2 #i #HLK1 #_ #HVW2 #IHV12 #L2 #HL12
-  elim (lsubr_fwd_ldrop2_abbr … HL12 … HLK1) -L1 *
+  elim (lsubr_fwd_drop2_abbr … HL12 … HLK1) -L1 *
   /3 width=6 by cpr_delta/
-|3,7: /4 width=1 by lsubr_bind, cpr_bind, cpr_beta/
-|4,6: /3 width=1 by cpr_flat, cpr_tau/
-|5,8: /4 width=3 by lsubr_bind, cpr_zeta, cpr_theta/
+|3,7: /4 width=1 by lsubr_pair, cpr_bind, cpr_beta/
+|4,6: /3 width=1 by cpr_flat, cpr_eps/
+|5,8: /4 width=3 by lsubr_pair, cpr_zeta, cpr_theta/
 ]
 qed-.
 
@@ -89,20 +88,25 @@ lemma cpr_delift: ∀G,K,V,T1,L,d. ⇩[d] L ≡ (K.ⓓV) →
   elim (lift_split … HVW i i) /3 width=6 by cpr_delta, ex2_2_intro/
 | * [ #a ] #I #W1 #U1 #IHW1 #IHU1 #L #d #HLK
   elim (IHW1 … HLK) -IHW1 #W2 #W #HW12 #HW2
-  [ elim (IHU1 (L. ⓑ{I}W1) (d+1)) -IHU1 /3 width=9 by ldrop_drop, cpr_bind, lift_bind, ex2_2_intro/
+  [ elim (IHU1 (L. ⓑ{I}W1) (d+1)) -IHU1 /3 width=9 by drop_drop, cpr_bind, lift_bind, ex2_2_intro/
   | elim (IHU1 … HLK) -IHU1 -HLK /3 width=8 by cpr_flat, lift_flat, ex2_2_intro/
   ]
 ]
 qed-.
 
-lemma cpr_append: ∀G. l_appendable_sn … (cpr G).
-#G #K #T1 #T2 #H elim H -G -K -T1 -T2
-/2 width=3 by cpr_bind, cpr_flat, cpr_zeta, cpr_tau, cpr_beta, cpr_theta/
-#G #K #K0 #V1 #V2 #W2 #i #HK0 #_ #HVW2 #IHV12 #L
-lapply (ldrop_fwd_length_lt2 … HK0) #H
-@(cpr_delta … (L@@K0) V1 … HVW2) //
-@(ldrop_O1_append_sn_le … HK0) /2 width=2 by lt_to_le/ (**) (* /3/ does not work *)
-qed.
+fact lstas_cpr_aux: ∀h,G,L,T1,T2,l. ⦃G, L⦄ ⊢ T1 •*[h, l] T2 →
+                    l = 0 → ⦃G, L⦄ ⊢ T1 ➡ T2.
+#h #G #L #T1 #T2 #l #H elim H -G -L -T1 -T2 -l
+/3 width=1 by cpr_eps, cpr_flat, cpr_bind/
+[ #G #L #l #k #H0 destruct normalize //
+| #G #L #K #V1 #V2 #W2 #i #l #HLK #_ #HVW2 #IHV12 #H destruct
+  /3 width=6 by cpr_delta/
+| #G #L #K #V1 #V2 #W2 #i #l #_ #_ #_ #_ <plus_n_Sm #H destruct
+]
+qed-.
+
+lemma lstas_cpr: ∀h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 •*[h, 0] T2 → ⦃G, L⦄ ⊢ T1 ➡ T2.
+/2 width=4 by lstas_cpr_aux/ qed.
 
 (* Basic inversion lemmas ***************************************************)
 
@@ -294,23 +298,6 @@ elim (cpr_inv_bind1 … H) -H *
 ]
 qed-.
 
-lemma cpr_fwd_shift1: ∀G,L1,L,T1,T. ⦃G, L⦄ ⊢ L1 @@ T1 ➡ T →
-                      ∃∃L2,T2. |L1| = |L2| & T = L2 @@ T2.
-#G #L1 @(lenv_ind_dx … L1) -L1 normalize
-[ #L #T1 #T #HT1
-  @(ex2_2_intro … (⋆)) // (**) (* explicit constructor *)
-| #I #L1 #V1 #IH #L #T1 #X
-  >shift_append_assoc normalize #H
-  elim (cpr_inv_bind1 … H) -H *
-  [ #V0 #T0 #_ #HT10 #H destruct
-    elim (IH … HT10) -IH -HT10 #L2 #T2 #HL12 #H destruct
-    >append_length >HL12 -HL12
-    @(ex2_2_intro … (⋆.ⓑ{I}V0@@L2) T2) [ >append_length ] /2 width=3 by trans_eq/ (**) (* explicit constructor *)
-  | #T #_ #_ #H destruct
-  ]
-]
-qed-.
-
 (* Basic_1: removed theorems 11:
             pr0_subst0_back pr0_subst0_fwd pr0_subst0
             pr2_head_2 pr2_cflat clear_pr2_trans
@@ -318,6 +305,6 @@ qed-.
             pr2_gen_ctail pr2_ctail
 *)
 (* Basic_1: removed local theorems 4:
-            pr0_delta_tau pr0_cong_delta
+            pr0_delta_eps pr0_cong_delta
             pr2_free_free pr2_free_delta
 *)