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Proof step 22 from proof valid-recs-next-update (previous step)

# wlar = # apebs, wlar[m3].status = used, subarray(wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)], 0, m + 1)[m6] = wl-entry(m11, stat), recs[v0 × m7] = recovery-entry(m6, m9), apebs[m] = mkpeb(aehdr, avidhdr(apebs[m3].vidhdr.vol, apebs[m3].vidhdr.leb, m0, m1, m5), buf, m2, boolvar), recs[apebs[m3].vidhdr.vol × apebs[m3].vidhdr.leb] = recovery-entry(m3, m4), subarray(apebs, 0, m + 1)[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), m3 + 1 < # apebs, m < # apebs, m3 < m, m3 < # apebs, v0 × m7 ∈ recs, apebs[m3].vidhdr.vol × apebs[m3].vidhdr.leb ∈ recs, ∀ ladr, m6. ladr ∈ recs ∧ recs[ladr].pnum = m6 ↔ wlar[m6].status = used ∧ m6 < m ∧ apebs[m6].vidhdr.vol = ladr.vol ∧ apebs[m6].vidhdr.leb = ladr.leb ⊦ v0 × m7 = apebs[m3].vidhdr.vol × apebs[m3].vidhdr.leb, stat = used ∧ ¬ m < m6 ∧ avhdr.vol = v0 ∧ avhdr.leb = m7

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 23:
# wlar = # apebs, wlar[m3].status = used, subarray(apebs, 0, m + 1)[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), recs[avhdr0.vol × avhdr0.leb] = recovery-entry(m3, m4), apebs[m] = mkpeb(aehdr, avidhdr(avhdr0.vol, avhdr0.leb, m0, m1, m5), buf, m2, boolvar), recs[v0 × m7] = recovery-entry(m6, m9), subarray(wlar[m, wl-entry(n0, used)][m3, wl-entry(n1, erasing)], 0, m + 1)[m6] = wl-entry(m11, stat), apebs[m3] = mkpeb(aehdr1, avhdr0, buf1, m8, boolvar1), m3 < # apebs, m3 < m, m < # apebs, m3 + 1 < # apebs, avhdr0.vol × avhdr0.leb ∈ recs, v0 × m7 ∈ recs, ∀ ladr, m6. ladr ∈ recs ∧ recs[ladr].pnum = m6 ↔ wlar[m6].status = used ∧ m6 < m ∧ apebs[m6].vidhdr.vol = ladr.vol ∧ apebs[m6].vidhdr.leb = ladr.leb ⊦ v0 × m7 = avhdr0.vol × avhdr0.leb, stat = used ∧ ¬ m < m6 ∧ avhdr.vol = v0 ∧ avhdr.leb = m7

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[m3], aehdr1, avhdr0, buf1, m8, boolvar1]

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[m3], aehdr1, avhdr0, buf1, m8, boolvar1