matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_cpx.ma

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  14
  15 include "basic_2/rt_transition/cpx_feqx.ma".
  16 include "basic_2/rt_computation/lpxs_cpxs.ma".
  17 include "basic_2/rt_computation/fpbs_lpxs.ma".
  18
  19 (* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
  20
  21 (* Properties with unbound context-sensitive parallel rt-transition *********)
  22
  23 (* Basic_2A1: uses: fpbs_cpx_trans_neq *)
  24 lemma fpbs_cpx_tneqx_trans: ∀h,G1,G2,L1,L2,T1,T2. ❪G1,L1,T1❫ ≥[h] ❪G2,L2,T2❫ →
  25                             ∀U2. ❪G2,L2❫ ⊢ T2 ⬈[h] U2 → (T2 ≛ U2 → ⊥) →
  26                             ∃∃U1. ❪G1,L1❫ ⊢ T1 ⬈[h] U1 & T1 ≛ U1 → ⊥ & ❪G1,L1,U1❫ ≥[h] ❪G2,L2,U2❫.
  27 #h #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 #HnTU2
  28 elim (fpbs_inv_star … H) -H #G0 #L0 #L3 #T0 #T3 #HT10 #H10 #HL03 #H32
  29 elim (feqx_cpx_trans … H32 … HTU2) -HTU2 #T4 #HT34 #H42
  30 lapply (feqx_tneqx_repl_dx … H32 … H42 … HnTU2) -T2 #HnT34
  31 lapply (lpxs_cpx_trans … HT34 … HL03) -HT34 #HT34
  32 elim (fqus_cpxs_trans_tneqx … H10 … HT34 HnT34) -T3 #T2 #HT02 #HnT02 #H24
  33 elim (teqx_dec T1 T0) [ #H10 | -HnT02 #HnT10 ]
  34 [ lapply (cpxs_trans … HT10 … HT02) -HT10 -HT02 #HT12
  35   elim (cpxs_tneqx_fwd_step_sn … HT12) [2: /3 width=3 by teqx_canc_sn/ ] -T0 -HT12
  36 | elim (cpxs_tneqx_fwd_step_sn … HT10 … HnT10) -HT10 -HnT10
  37 ]
  38 /4 width=16 by fpbs_intro_star, cpxs_teqx_fpbs_trans, ex3_intro/
  39 qed-.