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

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  14
  15 include "basic_2/notation/relations/btpred_7.ma".
  16 include "basic_2/s_transition/fquq.ma".
  17 include "basic_2/rt_transition/lfpr_lfpx.ma".
  18
  19 (* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
  20
  21 (* Basic_2A1: includes: fpbq_lleq *)
  22 inductive fpbq (h) (G1) (L1) (T1): relation3 genv lenv term ≝
  23 | fpbq_fquq: ∀G2,L2,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ → fpbq h G1 L1 T1 G2 L2 T2
  24 | fpbq_cpx : ∀T2. ⦃G1, L1⦄ ⊢ T1 ⬈[h] T2 → fpbq h G1 L1 T1 G1 L1 T2
  25 | fpbq_lfpx: ∀L2. ⦃G1, L1⦄ ⊢ ⬈[h, T1] L2 → fpbq h G1 L1 T1 G1 L2 T1
  26 .
  27
  28 interpretation
  29    "parallel rst-transition (closure)"
  30    'BTPRed h G1 L1 T1 G2 L2 T2 = (fpbq h G1 L1 T1 G2 L2 T2).
  31
  32 (* Basic properties *********************************************************)
  33
  34 lemma fpbq_refl: ∀h. tri_reflexive … (fpbq h).
  35 /2 width=1 by fpbq_cpx/ qed.
  36
  37 (* Basic_2A1: includes: cpr_fpbq *)
  38 lemma cpm_fpbq: ∀n,h,G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡[n, h] T2 → ⦃G, L, T1⦄ ≽[h] ⦃G, L, T2⦄.
  39 /3 width=2 by fpbq_cpx, cpm_fwd_cpx/ qed.
  40
  41 lemma lfpr_fpbq: ∀h,G,L1,L2,T. ⦃G, L1⦄ ⊢ ➡[h, T] L2 → ⦃G, L1, T⦄ ≽[h] ⦃G, L2, T⦄.
  42 /3 width=1 by fpbq_lfpx, lfpr_fwd_lfpx/ qed.
  43
  44 (* Basic_2A1: removed theorems 2:
  45               fpbq_fpbqa fpbqa_inv_fpbq
  46 *)