milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / fpr / fpcs_cpcs.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpr/fpcs_cpcs.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpr/fpcs_cpcs.etc
deleted file mode 100644 (file)
index b1288f7..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpr/fpcs_cpcs.etc
+++ /dev/null
@@ -1,86 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "basic_2/computation/fprs_cprs.ma".
-include "basic_2/equivalence/cpcs_cpcs.ma".
-include "basic_2/equivalence/fpcs_fpcs.ma".
-
-(* CONTEXT-FREE PARALLEL EQUIVALENCE ON CLOSURES ****************************)
-
-(* Advanced properties ******************************************************)
-
-lemma fpcs_flat_dx_tpr: ∀L1,L2,T1,T2. ⦃L1, T1⦄ ⬌* ⦃L2, T2⦄ → ∀V1,V2. V1 ➡ V2 →
-                        ∀I. ⦃L1, ⓕ{I}V1.T1⦄ ⬌* ⦃L2, ⓕ{I}V2.T2⦄.
-#L1 #L2 #T1 #T2 #HT12
-elim (fpcs_inv_fprs … HT12) -HT12
-/3 width=6 by fprs_flat_dx_tpr, fprs_div/ (**) (* auto too slow without trace *)
-qed.
-
-lemma fpcs_shift: ∀I,L1,L2,V1,V2,T1,T2. ⦃L1, -ⓑ{I}V1.T1⦄ ⬌* ⦃L2, -ⓑ{I}V2.T2⦄ →
-                  ⦃L1.ⓑ{I}V1, T1⦄ ⬌* ⦃L2.ⓑ{I}V2, T2⦄.
-#I #L1 #L2 #V1 #V2 #T1 #T2 #H12
-elim (fpcs_inv_fprs … H12) -H12 #L #T #H1 #H2
-elim (fprs_bind2_minus … H1) -H1 #W1 #U1 #HTU1 #H destruct
-elim (fprs_bind2_minus … H2) -H2 #W2 #U2 #HTU2 #H destruct /2 width=4/
-qed.
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma fpcs_inv_shift: ∀I,L1,L2,V1,V2,T1,T2. ⦃L1.ⓑ{I}V1, T1⦄ ⬌* ⦃L2.ⓑ{I}V2, T2⦄ →
-                      ⦃L1, -ⓑ{I}V1.T1⦄ ⬌* ⦃L2, -ⓑ{I}V2.T2⦄.
-#I #L1 #L2 #V1 #V2 #T1 #T2 #H12
-elim (fpcs_inv_fprs … H12) -H12 #L #T #H1 #H2
-elim (fprs_inv_pair1 … H1) -H1 #K1 #U1 #_ #HTU1 #H destruct
-elim (fprs_inv_pair1 … H2) -H2 #K2 #U2 #_ #HTU2 #H destruct /2 width=4/
-qed-.
-
-(* Advanced forward lemmas **************************************************)
-
-lemma fpcs_fwd_bind_minus: ∀I,L1,L2,V1,V2,T1,T2. ⦃L1, -ⓑ{I}V1.T1⦄ ⬌* ⦃L2, -ⓑ{I}V2.T2⦄ →
-                           ∀b. ⦃L1, ⓑ{b,I}V1.T1⦄ ⬌* ⦃L2, ⓑ{b,I}V2.T2⦄.
-#I #L1 #L2 #V1 #V2 #T1 #T2 #H12 #b
-elim (fpcs_inv_fprs … H12) -H12 #L #T #H1 #H2
-elim (fprs_fwd_bind2_minus … H1 b) -H1 #W1 #U1 #HTU1 #H destruct
-elim (fprs_fwd_bind2_minus … H2 b) -H2 #W2 #U2 #HTU2 #H destruct /2 width=4/
-qed-.
-
-lemma fpcs_fwd_shift: ∀I,L1,L2,V1,V2,T1,T2. ⦃L1.ⓑ{I}V1, T1⦄ ⬌* ⦃L2.ⓑ{I}V2, T2⦄ →
-                      ∀b. ⦃L1, ⓑ{b,I}V1.T1⦄ ⬌* ⦃L2, ⓑ{b,I}V2.T2⦄.
-/3 width=1 by fpcs_inv_shift, fpcs_fwd_bind_minus/ qed-.
-
-lemma fpcs_fwd_abst24: ∀a,L1,L2,V1,V2,T1,T2. ⦃L1, ⓛ{a}V1.T1⦄ ⬌* ⦃L2, ⓛ{a}V2.T2⦄ →
-                       ∀b,I,W. ⦃L1, ⓑ{b,I}W.T1⦄ ⬌* ⦃L2, ⓑ{b,I}W.T2⦄.
-#a #L1 #L2 #V1 #V2 #T1 #T2 #H12 #b #I #W
-elim (fpcs_inv_fprs … H12) -H12 #L #U #H1 #H2
-elim (fprs_fwd_abst2 … H1 b I W) -H1 #W1 #U1 #HTU1 #H destruct
-elim (fprs_fwd_abst2 … H2 b I W) -H2 #W2 #U2 #HTU2 #H destruct /2 width=4/
-qed-.
-
-lemma fpcs_fwd_abst13: ∀L1,L2,V1,V2,T1,T2. ⦃L1.ⓛV1, T1⦄ ⬌* ⦃L2.ⓛV2, T2⦄ →
-                       ∀I,W. ⦃L1.ⓑ{I}W, T1⦄ ⬌* ⦃L2.ⓑ{I}W, T2⦄.
-/4 width=4 by fpcs_fwd_shift, fpcs_fwd_abst24, fpcs_shift/ qed-.
-
-(* Properties on context-sensitive parallel equivalence for terms ***********)
-
-lemma cpcs_fpcs: ∀L,T1,T2. L ⊢ T1 ⬌* T2 → ⦃L, T1⦄ ⬌* ⦃L, T2⦄.
-#L #T1 #T2 #H
-elim (cpcs_inv_cprs … H) -H /3 width=4 by fprs_div, cprs_fprs/ (**) (* too slow without trace *)
-qed.
-
-(* Inversion lemmas on context-sensitive parallel equivalence for terms *****)
-
-lemma fpcs_inv_cpcs: ∀L,T1,T2. ⦃L, T1⦄ ⬌* ⦃L, T2⦄ → L ⊢ T1 ⬌* T2.
-#L #T1 #T2 #H
-elim (fpcs_inv_fprs … H) -H /3 width=4 by cprs_div, fprs_fwd_cprs/
-qed-.