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Proof step 10 from proof lf-valid-recs-notin-eraseq (previous step)

wlar[n0].status = 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 elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
apebs[n0] = mkpeb(aehdr, avhdr, buf, m0, boolvar), recs[avhdr.vol × avhdr.leb] = recovery-entry(n0, n1), wlar[n0] = wl-entry(m1, stat), stat = 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

spec: wlentry name: elim-02 seq: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat) subst: [wle, m, stat] → [wlar[n0], m1, stat]

Additional information

Used simplifier rules: ⊦ m = wle.ec ∧ stat = wle.status ↔ wle = wl-entry(m, stat); (elim) Used terms: wlar[n0], m1, stat