(**************************************************************************)
include "basic_2/s_computation/fqus_fqup.ma".
(**************************************************************************)
include "basic_2/s_computation/fqus_fqup.ma".
include "basic_2/rt_computation/fpbs_fqus.ma".
(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
include "basic_2/rt_computation/fpbs_fqus.ma".
(* PARALLEL RST-COMPUTATION FOR CLOSURES ************************************)
lemma tdeq_fpbs_trans: ∀h,o,T1,T. T1 ≛[h, o] T →
∀G1,G2,L1,L2,T2. ⦃G1, L1, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
lemma tdeq_fpbs_trans: ∀h,o,T1,T. T1 ≛[h, o] T →
∀G1,G2,L1,L2,T2. ⦃G1, L1, T⦄ ≥[h, o] ⦃G2, L2, T2⦄ → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
lemma fpbs_tdeq_trans: ∀h,o,G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T⦄ →
∀T2. T ≛[h, o] T2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.
lemma fpbs_tdeq_trans: ∀h,o,G1,G2,L1,L2,T1,T. ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T⦄ →
∀T2. T ≛[h, o] T2 → ⦃G1, L1, T1⦄ ≥[h, o] ⦃G2, L2, T2⦄.