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Proof step 44 from proof prepost-get-peb (previous step)

# apebs = # 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), free-ecs(wlar) ≠ ∅ → free-ecs(wlar).min ∈ free-ecs(wlar) ⊦ # free-ecs(wlar) = 0, free-ecs(wlar) = ∅, vtblpnum0 ∈ q, VTBL_VOLID ∈ vols, ∃ m. m < # wlar ∧ wlar[m].ec < free-ecs(wlar).min + WL_THRESHOLD ∧ wlar[m].status = free

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
# apebs = # wlar, wlar[m].ec = free-ecs(wlar).min, wlar[m].status = free, 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) ⊦ # free-ecs(wlar) = 0, free-ecs(wlar) = ∅, vtblpnum0 ∈ q, VTBL_VOLID ∈ vols, ∃ m. m < # wlar ∧ wlar[m].ec < free-ecs(wlar).min + WL_THRESHOLD ∧ wlar[m].status = free

Rule argument

Additional information

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%⊦ n ∈ free-ecs(wlar) ↔ (∃ m. m < # wlar ∧ wlar[m].status = free ∧ wlar[m].ec = n); (s)