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

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  14
  15 include "static_2/static/feqg_fqus.ma".
  16 include "static_2/static/feqg_feqg.ma".
  17 include "basic_2/rt_transition/cpx_feqg.ma".
  18 include "basic_2/rt_transition/lpx_reqg.ma".
  19 include "basic_2/rt_transition/fpb.ma".
  20
  21 (* PARALLEL RST-TRANSITION FOR CLOSURES *************************************)
  22
  23 (* Propreties with generic equivalence on referred closures *****************)
  24
  25 (* Basic_2A1: includes: fleq_fpbq fpbq_lleq *)
  26 (* Basic_2A1: uses: fpbq_feqx *)
  27 lemma feqg_fpb (S) (G1) (G2) (L1) (L2) (T1) (T2):
  28       reflexive … S → symmetric … S →
  29       ❪G1,L1,T1❫ ≛[S] ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫.
  30 #S #G1 #G2 #L1 #L2 #T1 #T2 #HS1 #HS2 #H
  31 elim (feqg_inv_gen_sn … H) -H #H #HL12 #HT12 destruct
  32 /4 width=8 by reqg_rpx, teqg_cpx, fpb_intro/
  33 qed.
  34
  35 lemma feqg_fpb_trans (S) (G) (L) (T):
  36       reflexive … S → symmetric … S → Transitive … S →
  37       ∀G1,L1,T1. ❪G1,L1,T1❫ ≛[S] ❪G,L,T❫ →
  38       ∀G2,L2,T2. ❪G,L,T❫ ≽ ❪G2,L2,T2❫ → ❪G1,L1,T1❫ ≽ ❪G2,L2,T2❫.
  39 #S #G #L #T #H1S #H2S #H3S #G1 #L1 #T1 #H1 #G2 #L2 #T2 #H2
  40 elim (fpb_inv_gen … H2) -H2 #L0 #T0 #H0 #HT02 #H
  41 elim (rpx_inv_reqg_lpx S … H) -H // #L3 #HL03 #HL32
  42 elim (feqg_fquq_trans … H1 … H0) -G -L -T // #G #L #T #H1 #H0
  43 lapply (feqg_cpx_trans_cpx … H0 … HT02) // -HT02 #HT2
  44 lapply (feqg_reqg_trans … H0 … HL03) -H0 -HL03 // #H
  45 elim (feqg_inv_gen_sn … H) -H #H #HL3 #_ destruct -T0
  46 /3 width=10 by fpb_intro, reqg_lpx_trans_rpx/
  47 qed-.