X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Flambda_delta%2FBasic_2%2Freducibility%2Fcpr.ma;h=0ad09e4b4c22a1bd0dec07b9ed2645d2a143a073;hb=011cf6478141e69822a5b40933f2444d0522532f;hp=90bd96d4d9cce6b223e97a590a3d1ec680fa9e86;hpb=d38087520d6ce1d696b28da40f3811291fc8a311;p=helm.git

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 90bd96d4d..0ad09e4b4 100644
--- a/matita/matita/contribs/lambda_delta/Basic_2/reducibility/cpr.ma
+++ b/matita/matita/contribs/lambda_delta/Basic_2/reducibility/cpr.ma
@@ -20,7 +20,7 @@ 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)"
@@ -28,69 +28,87 @@ interpretation
 
 (* Basic properties *********************************************************)
 
+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_pr: ∀T1,T2. T1 ⇒ T2 → ∀L. L ⊢ T1 ⇒ T2.
-/2/ qed.
+lemma cpr_pr: ∀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.
-/2/ qed.
+lemma cpr_refl: ∀L,T. L ⊢ T ➡ T.
+/2 width=1/ qed.
 
 (* Note: new property *)
 (* Basic_1: was only: pr2_thin_dx *) 
 lemma cpr_flat: ∀I,L,V1,V2,T1,T2.
-                L ⊢ V1 ⇒ V2 → L ⊢ T1 ⇒ T2 → L ⊢ 𝕗{I} V1. T1 ⇒ 𝕗{I} V2. T2.
+                L ⊢ V1 ➡ V2 → L ⊢ T1 ➡ T2 → L ⊢ ⓕ{I} V1. T1 ➡ ⓕ{I} V2. T2.
 #I #L #V1 #V2 #T1 #T2 * #V #HV1 #HV2 * /3 width=5/
 qed.
 
 lemma cpr_cast: ∀L,V,T1,T2.
-                L ⊢ T1 ⇒ T2 → L ⊢ 𝕔{Cast} V. T1 ⇒ T2.
-#L #V #T1 #T2 * /3/
+                L ⊢ T1 ➡ T2 → L ⊢ ⓣV. 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_conf: ∀L1,T1,T2. L1 ⊢ T1 ➡ T2 →
+                      ∀L2. L1 [0, |L1|] ≼ L2 → L2 ⊢ T1 ➡ T2.
 #L1 #T1 #T2 * #T #HT1 #HT2 #L2 #HL12 
-lapply (tpss_lsubs_conf … HT2 … HL12) -HT2 HL12 /3/
+lapply (tpss_lsubs_conf … HT2 … HL12) -HT2 -HL12 /3 width=4/
 qed.
 
 (* Basic inversion lemmas ***************************************************)
 
 (* Basic_1: was: pr2_gen_csort *)
-lemma cpr_inv_atom: ∀T1,T2. ⋆ ⊢ T1 ⇒ T2 → T1 ⇒ T2.
+lemma cpr_inv_atom: ∀T1,T2. ⋆ ⊢ T1 ➡ T2 → T1 ➡ T2.
 #T1 #T2 * #T #HT normalize #HT2
 <(tpss_inv_refl_O2 … HT2) -HT2 //
 qed-.
 
 (* Basic_1: was: pr2_gen_sort *)
-lemma cpr_inv_sort1: ∀L,T2,k. L ⊢ ⋆k ⇒ T2 → T2 = ⋆k.
+lemma cpr_inv_sort1: ∀L,T2,k. L ⊢ ⋆k ➡ T2 → T2 = ⋆k.
 #L #T2 #k * #X #H
 >(tpr_inv_atom1 … H) -H #H
 >(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: ∀L,V1,T1,U2. L ⊢ 𝕔{Cast} V1. T1 ⇒ U2 → (
-                        ∃∃V2,T2. L ⊢ V1 ⇒ V2 & L ⊢ T1 ⇒ T2 &
-                                 U2 = 𝕔{Cast} V2. T2
-                     ) ∨ L ⊢ T1 ⇒ U2.
+lemma cpr_inv_cast1: ∀L,V1,T1,U2. L ⊢ ⓣV1. T1 ➡ U2 → (
+                        ∃∃V2,T2. L ⊢ V1 ➡ V2 & L ⊢ T1 ➡ T2 &
+                                 U2 = ⓣV2. T2
+                     ) ∨ L ⊢ T1 ➡ U2.
 #L #V1 #T1 #U2 * #X #H #HU2
-elim (tpr_inv_cast1 … H) -H /3/
-* #V #T #HV1 #HT1 #H destruct -X;
-elim (tpss_inv_flat1 … HU2) -HU2 #V2 #T2 #HV2 #HT2 #H destruct -U2 /4 width=5/
+elim (tpr_inv_cast1 … H) -H /3 width=3/
+* #V #T #HV1 #HT1 #H destruct
+elim (tpss_inv_flat1 … HU2) -HU2 #V2 #T2 #HV2 #HT2 #H destruct /4 width=5/
 qed-.
 
-(* Basic_1: removed theorems 5: 
-            pr2_head_1 pr2_head_2 pr2_cflat pr2_gen_cflat clear_pr2_trans
+(* Basic_1: removed theorems 4: 
+            pr2_head_2 pr2_cflat pr2_gen_cflat clear_pr2_trans
    Basic_1: removed local theorems 3:
             pr2_free_free pr2_free_delta pr2_delta_delta
 *)
-
-(*
-pr2/fwd pr2_gen_appl
-pr2/fwd pr2_gen_abbr
-*)