matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_ffdeq.ma

   1 (**************************************************************************)
   2 (*       ___                                                              *)
   3 (*      ||M||                                                             *)
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  10 (*       \ /        This file is distributed under the terms of the       *)
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  13 (**************************************************************************)
  14
  15 include "basic_2/static/ffdeq.ma".
  16 include "basic_2/rt_transition/fpb_lfdeq.ma".
  17
  18 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
  19
  20 (* Properties with degree-based equivalence for closures ********************)
  21
  22 (* Basic_2A1: uses: fleq_fpb_trans *)
  23 lemma ffdeq_fpb_trans: ∀h,o,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≛[h, o] ⦃F2, K2, T2⦄ →
  24                        ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, o] ⦃G2, L2, U2⦄ →
  25                        ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, o] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≛[h, o] ⦃G2, L2, U2⦄.
  26 #h #o #F1 #F2 #K1 #K2 #T1 #T2 * -F2 -K2 -T2
  27 #K2 #T2 #HK12 #HT12 #G2 #L2 #U2 #H12
  28 elim (tdeq_fpb_trans … HT12 … H12) -T2 #K0 #T0 #H #HT0 #HK0
  29 elim (lfdeq_fpb_trans … HK12 … H) -K2 #L0 #U0 #H #HUT0 #HLK0
  30 @(ex2_3_intro … H) -H (**) (* full auto too slow *)
  31 /4 width=3 by ffdeq_intro_dx, lfdeq_trans, tdeq_lfdeq_conf, tdeq_trans/
  32 qed-.
  33
  34 (* Inversion lemmas with degree-based equivalence for closures **************)
  35 (*
  36 (* Basic_2A1: uses: fpb_inv_fleq *)
  37 lemma fpb_inv_ffdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
  38                      ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⊥.
  39 #h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
  40 [ #G2 #L2 #T2 #H12 #H elim (ffdeq_inv_gen_sn … H) -H
  41   #_ #H1 #H2
  42 (*
  43
  44   /3 width=8 by lfdeq_fwd_length, fqu_inv_eq/
  45 *)
  46 | #T2 #_ #HnT #H elim (ffdeq_inv_gen_sn … H) -H /2 width=1 by/
  47 | #L2 #_ #HnL #H elim (ffdeq_inv_gen_sn … H) -H /2 width=1 by/
  48 ]
  49 qed-.
  50 *)