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Proof step 6 from proof valid-recs-next-samerecs (previous step)

# wlar = # apebs, recs[v × m2] = recovery-entry(m3, m4), m < # apebs, ∀ ladr, m1. ladr ∈ recs ∧ recs[ladr].pnum = m1 ↔ wlar[m1].status = used ∧ m1 < m ∧ apebs[m1].vidhdr.vol = ladr.vol ∧ apebs[m1].vidhdr.leb = ladr.leb ⊦ v × m2 ∈ recs ∧ m3 = m1 ↔ subarray(wlar[m, wl-entry(m0, stat)], 0, m + 1)[m1].status = used ∧ ¬ m < m1 ∧ subarray(apebs, 0, m + 1)[m1].vidhdr.vol = v ∧ subarray(apebs, 0, m + 1)[m1].vidhdr.leb = m2, stat = used

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 7:
# wlar = # apebs, recs[v × m2] = recovery-entry(m3, m4), subarray(apebs, 0, m + 1)[m1] = mkpeb(aehdr, avhdr, buf, m5, boolvar), m < # apebs, ∀ ladr, m1. ladr ∈ recs ∧ recs[ladr].pnum = m1 ↔ wlar[m1].status = used ∧ m1 < m ∧ apebs[m1].vidhdr.vol = ladr.vol ∧ apebs[m1].vidhdr.leb = ladr.leb ⊦ v × m2 ∈ recs ∧ m3 = m1 ↔ subarray(wlar[m, wl-entry(m0, stat)], 0, m + 1)[m1].status = used ∧ ¬ m < m1 ∧ avhdr.vol = v ∧ avhdr.leb = m2, stat = used

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] → [subarray(apebs, 0, m + 1)[m1], aehdr, avhdr, buf, m5, 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: subarray(apebs, 0, m + 1)[m1], aehdr, avhdr, buf, m5, boolvar