matita/matita/contribs/lambdadelta/basic_2/computation/fpbs_ext.ma

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  14
  15 include "basic_2/computation/fpbs_alt.ma".
  16
  17 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
  18
  19 (* Properties on extended context-sensitive parallel computation for terms **)
  20
  21 lemma fpbs_cpxs_trans_neq: ∀h,g,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≥[h, g] ⦃G2, L2, T2⦄ →
  22                            ∀U2. ⦃G2, L2⦄ ⊢ T2 ➡*[h, g] U2 → (T2 = U2 → ⊥) →
  23                            ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ➡*[h, g] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ≥[h, g] ⦃G2, L2, U2⦄.
  24 #h #g #G1 #G2 #L1 #L2 #T1 #T2 #H #U2 #HTU2 #HnTU2 elim (fpbs_fpbsa … H) -H
  25 #L0 #T0 #HT10 #H10 #HL02 elim (eq_term_dec T1 T0) [ -HT10 | -HnTU2 ]
  26 [ #H destruct lapply (lpxs_cpxs_trans … HTU2 … HL02) -HTU2
  27   #HTU2 elim (fqus_cpxs_trans_neq … H10 … HTU2 HnTU2) -T2
  28   /3 width=6 by fqus_lpxs_fpbs, ex3_intro/
  29 | /4 width=6 by fpbs_cpxs_trans, fqus_lpxs_fpbs, ex3_intro/
  30 ]
  31 qed-.