matita/matita/contribs/lambdadelta/basic_2/computation/fpbg_fpns.ma

   1 (**************************************************************************)
   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       *)
  11 (*        v         GNU General Public License Version 2                  *)
  12 (*                                                                        *)
  13 (**************************************************************************)
  14
  15 include "basic_2/computation/fpbc_fpns.ma".
  16 include "basic_2/computation/fpbg.ma".
  17
  18 (* GENEARAL "BIG TREE" PROPER PARALLEL COMPUTATION FOR CLOSURES *************)
  19
  20 (* Properties on parallel computation for "big tree" normal forms ***********)
  21
  22 lemma fpbg_fpns_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G, L, T⦄ →
  23                        ∀G2,L2,T2. ⦃G, L, T⦄ ⊢ ⋕➡*[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄.
  24 #h #g #G1 #G #L1 #L #T1 #T #H @(fpbg_ind … H) -G -L -T
  25 [ /3 width=5 by fpbc_fpbg, fpbc_fpns_trans/
  26 | /4 width=9 by fpbg_strap1, fpbc_fpns_trans/
  27 ]
  28 qed-.
  29
  30 lemma fpns_fpbg_trans: ∀h,g,G,G2,L,L2,T,T2. ⦃G, L, T⦄ >⋕[h, g] ⦃G2, L2, T2⦄ →
  31                        ∀G1,L1,T1. ⦃G1, L1, T1⦄ ⊢ ⋕➡*[h, g] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄.
  32 #h #g #G #G2 #L #L2 #T #T2 #H @(fpbg_ind_dx … H) -G -L -T
  33 [ /3 width=5 by fpbc_fpbg, fpns_fpbc_trans/
  34 | /4 width=9 by fpbg_strap2, fpns_fpbc_trans/
  35 ]
  36 qed-.
  37
  38 lemma fpbs_fpbg: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
  39                  ⦃G1, L1, T1⦄ ⊢ ⋕➡*[h, g] ⦃G2, L2, T2⦄ ∨
  40                  ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄.
  41 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H @(fpbs_ind … H) -G2 -L2 -T2
  42 [ /2 width=1 by or_introl/
  43 | #G #G2 #L #L2 #T #T2 #_ #H2 * #H1 elim (fpb_fpbu … H2) -H2 #H2
  44   [ /3 width=5 by fpns_trans, or_introl/
  45   | /5 width=5 by fpbc_fpbg, fpns_fpbc_trans, fpbu_fpbc, or_intror/
  46   | /3 width=5 by fpbg_fpns_trans, or_intror/
  47   | /4 width=5 by fpbg_strap1, fpbu_fpbc, or_intror/
  48   ]
  49 ]
  50 qed-.
  51
  52 (* Advanced properties ******************************************************)
  53
  54 lemma fpbg_fpb_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
  55                       ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ ≽[h, g] ⦃G2, L2, T2⦄ →
  56                       ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄.
  57 #h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 #H2 elim (fpb_fpbu … H2) -H2
  58 /3 width=5 by fpbg_fpns_trans, fpbg_strap1, fpbu_fpbc/
  59 qed-.
  60
  61
  62 lemma fpb_fpbg_trans: ∀h,g,G1,G,G2,L1,L,L2,T1,T,T2.
  63                       ⦃G1, L1, T1⦄ ≽[h, g] ⦃G, L, T⦄ → ⦃G, L, T⦄ >⋕[h, g] ⦃G2, L2, T2⦄ →
  64                       ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄.
  65 #h #g #G1 #G #G2 #L1 #L #L2 #T1 #T #T2 #H1 elim (fpb_fpbu … H1) -H1
  66 /3 width=5 by fpns_fpbg_trans, fpbg_strap2, fpbu_fpbc/
  67 qed-.
  68
  69 lemma fpbs_fpbg_trans: ∀h,g,G1,G,L1,L,T1,T. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G, L, T⦄ →
  70                        ∀G2,L2,T2. ⦃G, L, T⦄ >⋕[h, g] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄.
  71 #h #g #G1 #G #L1 #L #T1 #T #H @(fpbs_ind … H) -G -L -T /3 width=5 by fpb_fpbg_trans/
  72 qed-.
  73
  74 (* Note: this is used in the closure proof *)
  75 lemma fpbg_fpbs_trans: ∀h,g,G,G2,L,L2,T,T2. ⦃G, L, T⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
  76                        ∀G1,L1,T1. ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G, L, T⦄ → ⦃G1, L1, T1⦄ >⋕[h, g] ⦃G2, L2, T2⦄.
  77 #h #g #G #G2 #L #L2 #T #T2 #H @(fpbs_ind_dx … H) -G -L -T /3 width=5 by fpbg_fpb_trans/
  78 qed-.