update in ground_2 static_2 basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / cpmhe.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpmhe.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpmhe.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/notation/relations/predevalstar_6.ma".
+include "basic_2/rt_transition/cnh.ma".
+include "basic_2/rt_computation/cpms.ma".
+
+(* HEAD T-UNBOUND EVALUATION FOR T-BOUND RT-TRANSITION ON TERMS *************)
+
+definition cpmhe (h) (n) (G) (L): relation2 term term ≝
+           λT1,T2. ∧∧ ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 & ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃T2⦄.
+
+interpretation "t-unbound evaluation for t-bound context-sensitive parallel rt-transition (term)"
+   'PRedEvalStar h n G L T1 T2 = (cpmhe h n G L T1 T2).
+
+definition R_cpmhe (h) (G) (L) (T): predicate nat ≝
+           λn. ∃U. ⦃G,L⦄ ⊢ T ➡*[h,n] 𝐍*⦃U⦄.
+
+(* Basic properties *********************************************************)
+
+lemma cpmhe_intro (h) (n) (G) (L):
+      ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G,L⦄ ⊢ ⥲[h] 𝐍⦃T2⦄ → ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍*⦃T2⦄.
+/2 width=1 by conj/ qed.
+
+(* Advanced properties ******************************************************)
+
+lemma cpmhe_sort (h) (n) (G) (L) (T):
+      ∀s. ⦃G,L⦄ ⊢ T ➡*[n,h] ⋆s → ⦃G,L⦄ ⊢ T ➡*[h,n] 𝐍*⦃⋆s⦄.
+/3 width=5 by cnh_sort, cpmhe_intro/ qed.
+
+lemma cpmhe_ctop (h) (n) (G) (T):
+      ∀i. ⦃G,⋆⦄ ⊢ T ➡*[n,h] #i → ⦃G,⋆⦄ ⊢ T ➡*[h,n] 𝐍*⦃#i⦄.
+/3 width=5 by cnh_ctop, cpmhe_intro/ qed.
+
+lemma cpmhe_zero (h) (n) (G) (L) (T):
+      ∀I. ⦃G,L.ⓤ{I}⦄ ⊢ T ➡*[n,h] #0 → ⦃G,L.ⓤ{I}⦄ ⊢ T ➡*[h,n] 𝐍*⦃#0⦄.
+/3 width=6 by cnh_zero, cpmhe_intro/ qed.
+
+lemma cpmhe_gref (h) (n) (G) (L) (T):
+      ∀l. ⦃G,L⦄ ⊢ T ➡*[n,h] §l → ⦃G,L⦄ ⊢ T ➡*[h,n] 𝐍*⦃§l⦄.
+/3 width=5 by cnh_gref, cpmhe_intro/ qed.
+
+lemma cpmhe_abst (h) (n) (p) (G) (L) (T):
+      ∀W,U. ⦃G,L⦄ ⊢ T ➡*[n,h] ⓛ{p}W.U → ⦃G,L⦄ ⊢ T ➡*[h,n] 𝐍*⦃ⓛ{p}W.U⦄.
+/3 width=5 by cnh_abst, cpmhe_intro/ qed.
+
+lemma cpmhe_abbr_neg (h) (n) (G) (L) (T):
+      ∀V,U. ⦃G,L⦄ ⊢ T ➡*[n,h] -ⓓV.U → ⦃G,L⦄ ⊢ T ➡*[h,n] 𝐍*⦃-ⓓV.U⦄.
+/3 width=5 by cnh_abbr_neg, cpmhe_intro/ qed.
+
+(* Basic forward lemmas *****************************************************)
+
+lemma cpmhe_fwd_cpms (h) (n) (G) (L):
+      ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡*[h,n] 𝐍*⦃T2⦄ → ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2.
+#h #n #G #L #T1 #T2 * #HT12 #_ //
+qed-.