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15 include "basic_2/computation/fpbs_alt.ma".
17 (* "BIG TREE" PARALLEL COMPUTATION FOR CLOSURES *****************************)
19 (* Properties on extended context-sensitive parallel computation for terms **)
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_inv_alt … H) -H
25 #L00 #L0 #T0 #HT10 #H10 #HL00 #HL02 lapply (lleq_cpxs_trans … HTU2 … HL02) -HTU2
26 #HTU2 lapply (cpxs_lleq_conf_sn … HTU2 … HL02) -HL02
27 #HL02 lapply (lpxs_cpxs_trans … HTU2 … HL00) -HTU2
28 #HTU2 elim (fqus_cpxs_trans_neq … H10 … HTU2 HnTU2) -H10 -HTU2 -HnTU2
29 #U0 #HTU0 #HnTU0 #HU02 elim (eq_term_dec T1 T0) [ -HT10 | -HnTU0 ]
30 [ #H destruct ] /3 width=10 by fpbs_intro_alt, ex3_intro/