matita/matita/contribs/lambdadelta/basic_2/etc_2A1/fpa/fpas_fpas.etc

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  14
  15 include "basic_2/substitution/fpa_fpa.ma".
  16 include "basic_2/multiple/fpas.ma".
  17
  18 (* MULTIPLE AJUSTMENT *******************************************************)
  19
  20 (* Advanced properties ******************************************************)
  21
  22 lemma fpas_strip: ∀L0,L1,L2,T0,T1,T2,s. ⦃L0, T0⦄ ⇳[s] ⦃L1, T1⦄ → ⦃L0, T0⦄ ⇳*[s] ⦃L2, T2⦄ →
  23                   ∃∃L,T. ⦃L1, T1⦄ ⇳*[s] ⦃L, T⦄ & ⦃L2, T2⦄ ⇳[s] ⦃L, T⦄.
  24 /3 width=4 by fpa_conf, bi_TC_strip/ qed-.
  25
  26 (* Main properties **********************************************************)
  27
  28 theorem fpas_conf: ∀s. bi_confluent … (fpas s).
  29 /3 width=4 by fpa_conf, bi_TC_confluent/ qed-.
  30
  31 theorem fpas_trans: ∀s. bi_transitive … (fpas s).
  32 /2 width=4 by bi_TC_transitive/ qed-.
  33
  34 theorem fpas_canc_sn: ∀L,L1,L2,T,T1,T2,s.
  35                       ⦃L, T⦄ ⇳*[s] ⦃L1, T1⦄→ ⦃L, T⦄ ⇳*[s] ⦃L2, T2⦄ → ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄.
  36 /3 width=4 by fpas_trans, fpas_sym/ qed-.
  37
  38 theorem fpas_canc_dx: ∀L1,L2,L,T1,T2,T,s.
  39                       ⦃L1, T1⦄ ⇳*[s] ⦃L, T⦄ → ⦃L2, T2⦄ ⇳*[s] ⦃L, T⦄ → ⦃L1, T1⦄ ⇳*[s] ⦃L2, T2⦄.
  40 /3 width=4 by fpas_trans, fpas_sym/ qed-.