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

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  14
  15 include "basic_2/rt_transition/fpb_feqg.ma".
  16 include "basic_2/rt_transition/fpbc.ma".
  17
  18 (* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
  19
  20 (* Properties with generic equivalence for closures *************************)
  21
  22 (* Basic_2A1: uses: teqg_fpb_trans lleq_fpb_trans fleq_fpb_trans *)
  23 lemma feqg_fpbc_trans (S) (G) (L) (T):
  24       reflexive … S → symmetric … S → Transitive … S →
  25       ∀G1,L1,T1. ❪G1,L1,T1❫ ≛[S] ❪G,L,T❫ →
  26       ∀G2,L2,T2. ❪G,L,T❫ ≻ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫.
  27 #S #G #L #T #H1S #H2S #H3S #G1 #L1 #T1 #H1 #G2 #L2 #T2 #H2
  28 elim (fpbc_inv_gen sfull … H2) -H2 #H2 #Hn2
  29 /6 width=9 by fpbc_intro, feqg_fpb_trans, feqg_canc_sn, feqg_feqx/
  30 qed-.
  31
  32 (* Inversion lemmas with generic equivalence for closures *******************)
  33
  34 (* Basic_2A1: uses: fpb_inv_fleq *)
  35 lemma fpbc_inv_feqg (S):
  36       ∀G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≻ ❪G2,L2,T2❫ →
  37       ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ⊥.
  38 #S #G1 #G2 #L1 #L2 #T1 #T2 #H #H12
  39 elim (fpbc_inv_gen S … H) -H #_ #Hn2
  40 /2 width=1 by/
  41 qed-.