milestone update in ground_2 and basic_2A

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/cpr.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/cpr.etc
deleted file mode 100644 (file)
index d82299c..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/cpr.etc
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-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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/unfold/tpss.ma".
-include "basic_2/reducibility/tpr.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
-
-(* Basic_1: includes: pr2_delta1 *)
-definition cpr: lenv → relation term ≝
-   λL,T1,T2. ∃∃T. T1 ➡ T & L ⊢ T ▶* [0, |L|] T2.
-
-interpretation
-   "context-sensitive parallel reduction (term)"
-   'PRed L T1 T2 = (cpr L T1 T2).
-
-(* Basic properties *********************************************************)
-
-lemma cpr_intro: ∀L,T1,T,T2,d,e. T1 ➡ T → L ⊢ T ▶* [d, e] T2 → L ⊢ T1 ➡ T2.
-/3 width=5/ 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.
-/3 width=5/ 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 ⊢ ⓕ{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 ⊢ ⓝ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_lsubr_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_lsubr_trans … 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.
-#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.
-#L #T2 #k * #X #H
->(tpr_inv_atom1 … H) -H #H
->(tpss_inv_sort1 … H) -H //
-qed-.
-
-(* Basic_1: was: pr2_gen_cast *)
-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 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 forward lemmas *****************************************************)
-
-lemma cpr_fwd_bind1_minus: ∀I,L,V1,T1,T. L ⊢ -ⓑ{I}V1.T1 ➡ T → ∀b.
-                           ∃∃V2,T2. L ⊢ ⓑ{b,I}V1.T1 ➡ ⓑ{b,I}V2.T2 &
-                                    T = -ⓑ{I}V2.T2.
-#I #L #V1 #T1 #T * #X #H1 #H2 #b
-elim (tpr_fwd_bind1_minus … H1 b) -H1 #V0 #T0 #HT10 #H destruct
-elim (tpss_inv_bind1 … H2) -H2 #V2 #T2 #HV02 #HT02 #H destruct /4 width=5/
-qed-.
-
-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
-   Basic_1: removed local theorems 3:
-            pr2_free_free pr2_free_delta pr2_delta_delta
-*)