matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/ltpr_ltpr.etc

   1 (**************************************************************************)
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   3 (*      ||M||                                                             *)
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  14
  15 include "basic_2/reducibility/tpr_tpr.ma".
  16 include "basic_2/reducibility/ltpr.ma".
  17
  18 (* CONTEXT-FREE PARALLEL REDUCTION ON LOCAL ENVIRONMENTS ********************)
  19
  20 (* Main properties **********************************************************)
  21
  22 theorem ltpr_conf: ∀L0:lenv. ∀L1. L0 ➡ L1 → ∀L2. L0 ➡ L2 →
  23                    ∃∃L. L1 ➡ L & L2 ➡ L.
  24 #L0 #L1 #H elim H -L0 -L1 /2 width=3/
  25 #I #K0 #K1 #V0 #V1 #_ #HV01 #IHK01 #L2 #H
  26 elim (ltpr_inv_pair1 … H) -H #K2 #V2 #HK02 #HV02 #H destruct
  27 elim (IHK01 … HK02) -K0 #K #HK1 #HK2
  28 elim (tpr_conf … HV01 HV02) -V0 /3 width=5/
  29 qed.