matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_fprs.ma

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   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
   4 (*      ||A||       A project by Andrea Asperti                           *)
   5 (*      ||T||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  14
  15 include "basic_2/dynamic/snv_fpr.ma".
  16
  17 (* STRATIFIED NATIVE VALIDITY FOR TERMS *************************************)
  18
  19 (* Properties on context-free parallel computation for closures *************)
  20
  21 fact ssta_fprs_aux: ∀h,g,n. (
  22                        ∀L,T2. ♯{L,T2} < n →
  23                        ∀T1. L ⊢ T1 ⬌* T2 → ⦃h, L⦄ ⊩ T1 :[g] → ⦃h, L⦄ ⊩ T2 :[g] →
  24                        ∀U1,l1. ⦃h, L⦄ ⊢ T1 •[g, l1] U1 →
  25                        ∀U2,l2. ⦃h, L⦄ ⊢ T2 •[g, l2] U2 →
  26                        L ⊢ U1 ⬌* U2 ∧ l1 = l2
  27                     ) → (
  28                        ∀L,T. ♯{L,T} < n → ⦃h, L⦄ ⊩ T :[g] →
  29                        ∀U. ⦃h, L⦄ ⊢ T •*➡*[g] U → ⦃h, L⦄ ⊩ U :[g]
  30                     ) → (
  31                        ∀L1,T1. ♯{L1,T1} < n →
  32                        ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U1 →
  33                        ∀L2,T2. ⦃L1, T1⦄ ➡* ⦃L2, T2⦄ →  ⦃h, L1⦄ ⊩ T1 :[g] →
  34                        ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g, l] U2 & ⦃L1, U1⦄ ⬌* ⦃L2, U2⦄
  35                     ) →
  36                     ∀L1,T1. ♯{L1,T1} = n →
  37                     ∀U1,l. ⦃h, L1⦄ ⊢ T1 •[g, l] U1 →
  38                     ∀L2,T2. ⦃L1, T1⦄ ➡* ⦃L2, T2⦄ → ⦃h, L1⦄ ⊩ T1 :[g] →
  39                     ∃∃U2. ⦃h, L2⦄ ⊢ T2 •[g, l] U2 & ⦃L1, U1⦄ ⬌* ⦃L2, U2⦄.
  40 #h #g #n #IH3 #IH2 #IH1 #L1 #T1 #Hn #U1 #l #HTU1 #L2 #T2 #H12 #HT1
  41 @(fprs_ind … H12) -L2 -T2 [-IH1 /2 width=3/ ] (**) (* auto fails without -IH1 *)
  42 #L #L2 #T #T2 #HT1 #HT2 * #U #HTU #HU1
  43 (*
  44 lapply (IH2 …
  45
  46 elim (ssta_fpr_aux … IH3 … Hn … HTU1 … HT2 HT1)
  47 -T1 -IH3 -IH2 -HL1 [2: /3 width=5/ ] -n #U #HTU #HU1
  48 *)