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Theorem rely-PROP_FO

⊦ ( ctrok(gs.fctr, gs.fwriters) ∧ writersOk(gs.bq, gs.pq, gs.fwriters) ∧ pendingOk(gs.bq, gs.pq) ∧ SFTrailing(gs.bq) ∧ readFOsOk(gs.rfo, gs.fwriters)) ∧ (∃ n. n < # gs.bq(tid) ∧ isPropFO(n, l, gs.bq(tid))) ∧ ⟨fwriters := gs.fwriters, pq := gs.pq, bq := gs.bq, rfo := gs.rfo; PROP_FO(tid, l, fwriters; pq, bq, rfo); gs := ((gs.pq:= pq).bq:= bq).rfo:= rfo⟩ (gs0 = gs) → (∀ t0. relyws(t0, gs.freaders, gs0.freaders) ∧ relyws(t0, gs.fwriters, gs0.fwriters) ∧ rely(t0, gs.pq, gs.bq, gs0.pq, gs0.bq) ∧ gs.bq(t0) ⊒w gs0.bq(t0) ∧ (gs.rfo(t0) = [] → gs0.rfo(t0) = []) ∧ (gs.rfo(t0) = gs.bq(t0) → gs0.rfo(t0) = gs0.bq(t0)) ∧ (gs.rfo(t0) + SF ' = gs.bq(t0) → gs0.rfo(t0) + SF ' = gs0.bq(t0) ∨ gs0.rfo(t0) = gs0.bq(t0)))

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