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

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  14
  15 include "basic_2/notation/relations/predsubty_6.ma".
  16 include "static_2/static/feqx.ma".
  17 include "static_2/s_transition/fquq.ma".
  18 include "basic_2/rt_transition/lpr_lpx.ma".
  19
  20 (* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
  21
  22 (* Basic_2A1: includes: fleq_fpbq fpbq_lleq *)
  23 inductive fpbq (G1) (L1) (T1): relation3 genv lenv term ≝
  24 | fpbq_fquq: ∀G2,L2,T2. ❪G1,L1,T1❫ ⬂⸮ ❪G2,L2,T2❫ → fpbq G1 L1 T1 G2 L2 T2
  25 | fpbq_cpx : ∀T2. ❪G1,L1❫ ⊢ T1 ⬈ T2 → fpbq G1 L1 T1 G1 L1 T2
  26 | fpbq_lpx : ∀L2. ❪G1,L1❫ ⊢ ⬈ L2 → fpbq G1 L1 T1 G1 L2 T1
  27 | fpbq_feqx: ∀G2,L2,T2. ❪G1,L1,T1❫ ≛ ❪G2,L2,T2❫ → fpbq G1 L1 T1 G2 L2 T2
  28 .
  29
  30 interpretation
  31   "parallel rst-transition (closure)"
  32   'PRedSubTy G1 L1 T1 G2 L2 T2 = (fpbq G1 L1 T1 G2 L2 T2).
  33
  34 (* Basic properties *********************************************************)
  35
  36 lemma fpbq_refl: tri_reflexive … fpbq.
  37 /2 width=1 by fpbq_cpx/ qed.
  38
  39 (* Basic_2A1: includes: cpr_fpbq *)
  40 lemma cpm_fpbq (h) (n) (G) (L):
  41       ∀T1,T2. ❪G,L❫ ⊢ T1 ➡[h,n] T2 → ❪G,L,T1❫ ≽ ❪G,L,T2❫.
  42 /3 width=3 by fpbq_cpx, cpm_fwd_cpx/ qed.
  43
  44 lemma lpr_fpbq (h) (G) (T):
  45       ∀L1,L2. ❪G,L1❫ ⊢ ➡[h,0] L2 → ❪G,L1,T❫ ≽ ❪G,L2,T❫.
  46 /3 width=2 by fpbq_lpx, lpr_fwd_lpx/ qed.
  47
  48 (* Basic_2A1: removed theorems 2:
  49               fpbq_fpbqa fpbqa_inv_fpbq
  50 *)