- parallel reduction for local environments: we proved the equivalence

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/reducibility/lfpr_alt.ma b/matita/matita/contribs/lambda_delta/basic_2/reducibility/lfpr_alt.ma
index bfb483781044587c3af1e005256f3049cc514d83..adff7ad07cc353a2a3c78854b8ed77dee52988d1 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/reducibility/lfpr_alt.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/reducibility/lfpr_alt.ma
@@ -13,7 +13,8 @@
 (**************************************************************************)
 
 include "basic_2/grammar/lenv_px_bi.ma".
-include "basic_2/reducibility/fpr.ma".
+include "basic_2/reducibility/fpr_cpr.ma".
+include "basic_2/reducibility/lfpr_fpr.ma".
 
 (* FOCALIZED PARALLEL REDUCTION FOR LOCAL ENVIRONMENTS **********************)
 
@@ -29,6 +30,15 @@ interpretation
 lemma lfpra_refl: reflexive … lfpra.
 /2 width=1/ qed.
 
+lemma fpr_lfpra: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ➡ ⦃L2, T2⦄ → ⦃L1⦄ ➡➡ ⦃L2⦄.
+#L1 elim L1 -L1
+[ #L2 #T1 #T2 #H
+  elim (fpr_inv_atom1 … H) -H #_ #H destruct //
+| #L1 #I #V1 #IH #L2 #T1 #T2 #H
+  elim (fpr_inv_pair1 … H) -H #L #V #HV1 #HL1 #H destruct /3 width=3/
+]
+qed.
+
 (* Basic inversion lemmas ***************************************************)
 
 lemma lfpra_inv_atom1: ∀L2. ⦃⋆⦄ ➡➡ ⦃L2⦄ → L2 = ⋆.
@@ -47,48 +57,23 @@ lemma lfpra_inv_pair2: ∀L1,K2,I,V2. ⦃L1⦄ ➡➡ ⦃K2. ⓑ{I} V2⦄ →
                                 L1 = K1. ⓑ{I} V1.
 /2 width=1 by lpx_bi_inv_pair2/ qed-.
 
+lemma lfpra_inv_fpr: ∀L1,L2. ⦃L1⦄ ➡➡ ⦃L2⦄ → ∀T.⦃L1, T⦄ ➡ ⦃L2, T⦄.
+#L1 #L2 * -L1 -L2 // /3 width=1/
+qed-.
+
 (* Basic forward lemmas *****************************************************)
 
 lemma lfpra_fwd_length: ∀L1,L2. ⦃L1⦄ ➡➡ ⦃L2⦄ → |L1| = |L2|.
 /2 width=2 by lpx_bi_fwd_length/ qed-.
 
-(****************************************************************************)
-(*
-lemma fpr_lfpra: ∀L1,T1,L2,T2. ⦃L1, T1⦄ ➡ ⦃L2, T2⦄ → ⦃L1⦄ ➡➡ ⦃L2⦄.
-#L1 #T1 @(cw_wf_ind … L1 T1) -L1 -T1 *
-[ #T1 #_ #L2 #T2 #H
-  elim (fpr_inv_atom1 … H) -H #_ #H destruct //
-| #L1 #I #V1 #T1 #IH #Y #X #H
-  elim (fpr_inv_pair1 … H) -H #L2 #V2 #HL12 #H destruct
-  @lpx_bi_pair 
-  [ @(IH … HL12) 
-  | @IH 
-  
-  /3 width=4/
+(* Main properties **********************************************************)
 
-lemma fpr_lfpra: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ➡ ⦃L2, T2⦄ → ⦃L1⦄ ➡➡ ⦃L2⦄.
-#L1 elim L1 -L1
-[ #L2 #T1 #T2 #H
-  elim (fpr_inv_atom1 … H) -H #_ #H destruct //
-| #L1 #I #V1 #IH #L2 #T1 #T2 #H
-  elim (fpr_inv_pair1 … H) -H #L #V #HL1 #H destruct
-  @lpx_bi_pair /2 width=3/ 
-  
-  /4 width=3/
-
-(*
-include "basic_2/reducibility/lcpr.ma".
-
-lemma lcpr_pair2: ∀L1,L2. L1 ⊢ ➡ L2 → ∀V1,V2. ⦃L1, V1⦄ ➡ ⦃L2, V2⦄ →
-                  ∀I. L1. ⓑ{I} V1 ⊢ ➡ L2. ⓑ{I} V2.
-#L1 #L2 * #L #HL1 #HL2 #V1 #V2 *
-#H1 #H2 #I
-@(ex2_1_intro … (L.ⓑ{I}V1)) /2 width=1/
-@tpss_
-
-(*
-<(ltpss_fwd_length … HL2) /4 width=5/
+theorem lfpr_lfpra: ∀L1,L2. ⦃L1⦄ ➡ ⦃L2⦄ → ⦃L1⦄ ➡➡ ⦃L2⦄.
+#L1 #L2 #H
+lapply (lfpr_inv_fpr … H (⋆0)) -H /2 width=3/
 qed.
-*)
-*)
-*)
\ No newline at end of file
+
+theorem lfpra_lfpr: ∀L1,L2. ⦃L1⦄ ➡➡ ⦃L2⦄ → ⦃L1⦄ ➡ ⦃L2⦄.
+#L1 #L2 #H
+lapply (lfpra_inv_fpr … H (⋆0)) -H /2 width=3/
+qed-.