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Proof step 42 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(apebs, q), valid-eraseq(wlar, q), valid-eraseq(q), valid-global-sqn(apebs, sqnum), valid-vtbl(apebs, vols, wlar, vtblpnum0), valid-wl(apebs, wlar) ⊦ # free-ecs(wlar) = 0, free-ecs(wlar) = ∅, VTBL_VOLID ∈ vols, vtblpnum0 ∈ q, ∃ m. m < # wlar ∧ wlar[m].ec < free-ecs(wlar).min + WL_THRESHOLD ∧ wlar[m].status = free

User applied rule apply lemma

And obtained the following new goals

Proof step 43:
⊦ ns ≠ ∅ → ns.min ∈ ns
Proof step 44:
# 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

Rule argument

spec: oset, inst: nat-set name: Min-in seq: ⊦ ns ≠ ∅ → ns.min ∈ ns subst: [ns] → [free-ecs(wlar)]

Additional information

Used terms: free-ecs(wlar)