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Proof step 12 from proof lf-valid-recs-notin-eraseq (previous step)

wlar[n0] = wl-entry(m1, used), recs[avhdr.vol × avhdr.leb] = recovery-entry(n0, n1), apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), n0 < # apebs, valid-eraseq(wlar, q), n0 ∈ q, avhdr.vol × avhdr.leb ∈ recs, ∀ ladr, m. ladr ∈ recs ∧ recs[ladr].pnum = m ↔ wlar[m].status = used ∧ m < # apebs ∧ apebs[m].vidhdr.vol = ladr.vol ∧ apebs[m].vidhdr.leb = ladr.leb ⊦ n0 = # apebs

Heuristic quantifier applied rule all left

And obtained the following new goals

Proof step 13:
avhdr.vol × avhdr.leb ∈ recs ∧ recs[avhdr.vol × avhdr.leb].pnum = # apebs ↔ wlar[# apebs].status = used ∧ # apebs < # apebs ∧ apebs[# apebs].vidhdr.vol = (avhdr.vol × avhdr.leb).vol ∧ apebs[# apebs].vidhdr.leb = (avhdr.vol × avhdr.leb).leb, apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), recs[avhdr.vol × avhdr.leb] = recovery-entry(n0, n1), wlar[n0] = wl-entry(m1, used), n0 < # apebs, valid-eraseq(wlar, q), avhdr.vol × avhdr.leb ∈ recs, n0 ∈ q, ∀ ladr, m. ladr ∈ recs ∧ recs[ladr].pnum = m ↔ wlar[m].status = used ∧ m < # apebs ∧ apebs[m].vidhdr.vol = ladr.vol ∧ apebs[m].vidhdr.leb = ladr.leb ⊦ n0 = # apebs

Rule argument

pos: left 8 terms: avhdr.vol × avhdr.leb, # apebs

Additional information

Used terms: avhdr.vol × avhdr.leb, # apebs