| # apebs = # wlar, n0 = free-ecs(wlar).min + WL_THRESHOLD, wlar0 = wlar, bflipset-cons(bflipset, wlar), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum0), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum0), valid-wl(apebs, wlar), ∃ m. m < # wlar ∧ wlar[m].ec < free-ecs(wlar).min + WL_THRESHOLD ∧ wlar[m].status = free ⊦ [ubi_wl_find_free_max_below#(free-ecs(wlar).min + WL_THRESHOLD, wlar; vtblpnum)] ( vtblpnum < # wlar0 ∧ wlar0[vtblpnum].status = free ∧ wlar0[vtblpnum].ec = below(free-ecs(wlar0), n0).max → ⟪err := ESUCCESS⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → vtblpnum < # apebs ∧ wlar[vtblpnum].status = free))), # free-ecs(wlar) = 0, free-ecs(wlar) = ∅, vtblpnum0 ∈ q, VTBL_VOLID ∈ vols |
# apebs = # wlar, wlar[m].status = free, # free-ecs(wlar) ≠ 0, free-ecs(wlar) ≠ ∅, wlar[m].ec < free-ecs(wlar).min + WL_THRESHOLD, m < # wlar, bflipset-cons(bflipset, wlar), ubi-io-inv(apebs), unique-sqns(apebs), valid-ebatbl(apebs, wlar, vols, vtblpnum0), valid-eraseq(q), valid-eraseq(wlar, q), valid-eraseq(apebs, q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum0), valid-wl(apebs, wlar), ¬ vtblpnum0 ∈ q, ¬ VTBL_VOLID ∈ vols ⊦ [ubi_wl_find_free_max_below#(free-ecs(wlar).min + WL_THRESHOLD, wlar; vtblpnum)] ( vtblpnum < # wlar ∧ wlar[vtblpnum].status = free ∧ wlar[vtblpnum].ec = below(free-ecs(wlar), free-ecs(wlar).min + WL_THRESHOLD).max → ⟪err := ESUCCESS⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → vtblpnum < # apebs)))
Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic