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Proof step 8 from proof lf-valid-recs-valid-peb (previous step)

# apebs = # wlar, wlar[n0].status = used, recs[apebs[n0].vidhdr.vol × apebs[n0].vidhdr.leb] = recovery-entry(n0, n1), n0 < m0, n0 < # wlar, valid-wl(subarray(apebs, 0, m0), subarray(wlar, 0, m0)), apebs[n0].vidhdr.vol × apebs[n0].vidhdr.leb ∈ recs, m0 ≤ # wlar ⊦ valid-peb(apebs[n0].vidhdr.vol, apebs[n0].vidhdr.leb, apebs[n0])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
# apebs = # wlar, wlar[n0].status = used, recs[avhdr.vol × avhdr.leb] = recovery-entry(n0, n1), apebs[n0] = mkpeb(aehdr, avhdr, buf, m, boolvar), n0 < # wlar, n0 < m0, valid-wl(subarray(apebs, 0, m0), subarray(wlar, 0, m0)), avhdr.vol × avhdr.leb ∈ recs, m0 ≤ # wlar ⊦ valid-peb(avhdr.vol, avhdr.leb, apebs[n0])

Rule argument

spec: apeb name: elim seq: ⊦ ( ( (aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar) subst: [apeb, aehdr, avhdr, buf, m, boolvar] → [apebs[n0], aehdr, avhdr, buf, m, boolvar]

Additional information

Used simplifier rules: ⊦ ( ((aehdr = apeb.echdr ∧ avhdr = apeb.vidhdr) ∧ buf = apeb.data) ∧ m = apeb.fill) ∧ (boolvar ↔ apeb.bad) ↔ apeb = mkpeb(aehdr, avhdr, buf, m, boolvar); (elim) Used terms: apebs[n0], aehdr, avhdr, buf, m, boolvar