- we introduced the pointer_step rc in the perspective of proving

[helm.git] / matita / matita / contribs / lambda_delta / basic_2 / reducibility / cpr.ma

diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/cpr.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/cpr.ma
index 953145592afe77e010941f053f3c60db33cde01c..22fbfc148440b49c722985a6ae9a518598942845 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/reducibility/cpr.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/reducibility/cpr.ma
@@ -12,7 +12,6 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/grammar/cl_shift.ma".
 include "basic_2/unfold/tpss.ma".
 include "basic_2/reducibility/tpr.ma".
 
@@ -20,7 +19,7 @@ include "basic_2/reducibility/tpr.ma".
 
 (* Basic_1: includes: pr2_delta1 *)
 definition cpr: lenv → relation term ≝
-   λL,T1,T2. ∃∃T. T1 ➡ T & L ⊢ T [0, |L|] ▶* T2.
+   λL,T1,T2. ∃∃T. T1 ➡ T & L ⊢ T ▶* [0, |L|] T2.
 
 interpretation
    "context-sensitive parallel reduction (term)"
@@ -28,14 +27,14 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-lemma cpr_intro: ∀L,T1,T,T2,d,e. T1 ➡ T → L ⊢ T [d, e] ▶* T2 → L ⊢ T1 ➡ T2.
+lemma cpr_intro: ∀L,T1,T,T2,d,e. T1 ➡ T → L ⊢ T ▶* [d, e] T2 → L ⊢ T1 ➡ T2.
 /4 width=3/ qed-.
 
 (* Basic_1: was by definition: pr2_free *)
 lemma cpr_tpr: ∀T1,T2. T1 ➡ T2 → ∀L. L ⊢ T1 ➡ T2.
 /2 width=3/ qed.
 
-lemma cpr_tpss: ∀L,T1,T2,d,e. L ⊢ T1 [d, e] ▶* T2 → L ⊢ T1 ➡ T2.
+lemma cpr_tpss: ∀L,T1,T2,d,e. L ⊢ T1 ▶* [d, e] T2 → L ⊢ T1 ➡ T2.
 /3 width=5/ qed.
 
 lemma cpr_refl: ∀L,T. L ⊢ T ➡ T.
@@ -49,16 +48,16 @@ lemma cpr_flat: ∀I,L,V1,V2,T1,T2.
 qed.
 
 lemma cpr_cast: ∀L,V,T1,T2.
-                L â\8a¢ T1 â\9e¡ T2 â\86\92 L â\8a¢ â\93£V. T1 ➡ T2.
+                L â\8a¢ T1 â\9e¡ T2 â\86\92 L â\8a¢ â\93\9dV. T1 ➡ T2.
 #L #V #T1 #T2 * /3 width=3/
 qed.
 
 (* Note: it does not hold replacing |L1| with |L2| *)
 (* Basic_1: was only: pr2_change *)
-lemma cpr_lsubs_conf: ∀L1,T1,T2. L1 ⊢ T1 ➡ T2 →
-                      ∀L2. L1 [0, |L1|] ≼ L2 → L2 ⊢ T1 ➡ T2.
+lemma cpr_lsubs_trans: ∀L1,T1,T2. L1 ⊢ T1 ➡ T2 →
+                       ∀L2. L2 ≼ [0, |L1|] L1 → L2 ⊢ T1 ➡ T2.
 #L1 #T1 #T2 * #T #HT1 #HT2 #L2 #HL12 
-lapply (tpss_lsubs_conf … HT2 … HL12) -HT2 -HL12 /3 width=4/
+lapply (tpss_lsubs_trans … HT2 … HL12) -HT2 -HL12 /3 width=4/
 qed.
 
 (* Basic inversion lemmas ***************************************************)
@@ -76,30 +75,10 @@ lemma cpr_inv_sort1: ∀L,T2,k. L ⊢ ⋆k ➡ T2 → T2 = ⋆k.
 >(tpss_inv_sort1 … H) -H //
 qed-.
 
-(* Basic_1: was pr2_gen_abbr *)
-lemma cpr_inv_abbr1: ∀L,V1,T1,U2. L ⊢ ⓓV1. T1 ➡ U2 →
-                     (∃∃V,V2,T2. V1 ➡ V & L ⊢ V [O, |L|] ▶* V2 &
-                                 L. ⓓV ⊢ T1 ➡ T2 &
-                                 U2 = ⓓV2. T2
-                      ) ∨
-                      ∃∃T. ⇧[0,1] T ≡ T1 & L ⊢ T ➡ U2.
-#L #V1 #T1 #Y * #X #H1 #H2
-elim (tpr_inv_abbr1 … H1) -H1 *
-[ #V #T0 #T #HV1 #HT10 #HT0 #H destruct
-  elim (tpss_inv_bind1 … H2) -H2 #V2 #T2 #HV2 #HT2 #H destruct
-  lapply (tps_lsubs_conf … HT0 (L. ⓓV) ?) -HT0 /2 width=1/ #HT0
-  lapply (tps_weak_all … HT0) -HT0 #HT0
-  lapply (tpss_lsubs_conf … HT2 (L. ⓓV) ?) -HT2 /2 width=1/ #HT2
-  lapply (tpss_weak_all … HT2) -HT2 #HT2
-  lapply (tpss_strap … HT0 HT2) -T /4 width=7/
-| /4 width=5/
-]
-qed-.
-
 (* Basic_1: was: pr2_gen_cast *)
-lemma cpr_inv_cast1: â\88\80L,V1,T1,U2. L â\8a¢ â\93£V1. T1 ➡ U2 → (
+lemma cpr_inv_cast1: â\88\80L,V1,T1,U2. L â\8a¢ â\93\9dV1. T1 ➡ U2 → (
                         ∃∃V2,T2. L ⊢ V1 ➡ V2 & L ⊢ T1 ➡ T2 &
-                                 U2 = â\93£V2. T2
+                                 U2 = â\93\9dV2. T2
                      ) ∨ L ⊢ T1 ➡ U2.
 #L #V1 #T1 #U2 * #X #H #HU2
 elim (tpr_inv_cast1 … H) -H /3 width=3/
@@ -107,9 +86,18 @@ elim (tpr_inv_cast1 … H) -H /3 width=3/
 elim (tpss_inv_flat1 … HU2) -HU2 #V2 #T2 #HV2 #HT2 #H destruct /4 width=5/
 qed-.
 
+(* Basic forward lemmas *****************************************************)
+
+lemma cpr_fwd_shift1: ∀L,L1,T1,T. L ⊢ L1 @@ T1 ➡ T →
+                      ∃∃L2,T2. |L1| = |L2| & T = L2 @@ T2.
+#L #L1 #T1 #T * #X #H1 #H2
+elim (tpr_fwd_shift1 … H1) -H1 #L0 #T0 #HL10 #H destruct
+elim (tpss_fwd_shift1 … H2) -H2 #L2 #T2 #HL02 #H destruct /2 width=4/
+qed-.
+
 (* Basic_1: removed theorems 6: 
             pr2_head_2 pr2_cflat pr2_gen_cflat clear_pr2_trans
-           pr2_gen_ctail pr2_ctail
+            pr2_gen_ctail pr2_ctail
    Basic_1: removed local theorems 3:
             pr2_free_free pr2_free_delta pr2_delta_delta
 *)