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[helm.git] / matita / matita / contribs / lambda-delta / Basic-2 / reduction / cpr_lift.ma
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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_lift.ma".
-include "Basic-2/reduction/tpr_lift.ma".
-include "Basic-2/reduction/cpr.ma".
-
-(* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
-
-(* Advanced properties ******************************************************)
-
-lemma cpr_delta: ∀L,K,V1,W1,W2,i.
-                 ↓[0, i] L ≡ K. 𝕓{Abbr} V1 → K ⊢ V1 [0, |L| - i - 1] ≫* W1 →
-                 ↑[0, i + 1] W1 ≡ W2 → L ⊢ #i ⇒ W2.
-#L #K #V1 #W1 #W2 #i #HLK #HVW1 #HW12
-@ex2_1_intro [2: // | skip | @tpss_subst /2 width=6/ ] (**) (* /4 width=6/ is too slow *)
-qed.
-
-(* Advanced inversion lemmas ************************************************)
-
-(* Basic-1: was: pr2_gen_lref *)
-lemma cpr_inv_lref1: ∀L,T2,i. L ⊢ #i ⇒ T2 →
-                     T2 = #i ∨
-                     ∃∃K,V1,T1. ↓[0, i] L ≡ K. 𝕓{Abbr} V1 &
-                                K ⊢ V1 [0, |L| - i - 1] ≫* T1 &
-                                ↑[0, i + 1] T1 ≡ T2 &
-                                i < |L|.
-#L #T2 #i * #X #H
->(tpr_inv_atom1 … H) -H #H
-elim (tpss_inv_lref1 … H) -H /2/
-* /3 width=6/
-qed.
-
-(* Basic-1: was: pr2_gen_abst *)
-lemma cpr_inv_abst1: ∀V1,T1,U2. 𝕔{Abst} V1. T1 ⇒ U2 →
-                     ∃∃V2,T2. V1 ⇒ V2 & T1 ⇒ T2 & U2 = 𝕔{Abst} V2. T2.
-/2/ qed.
-
-(* Relocation properties ****************************************************)
-
-(* Basic-1: was: pr2_lift *)
-
-(* Basic-1: was: pr2_gen_lift *)
-