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Proof step 45 from proof valid-recs-next-update (previous step)

# wlar = # apebs, wlar[m6] = wl-entry(m11, used), recs[v × n, recovery-entry(m, m0)][avhdr.vol × avhdr.leb] = recovery-entry(m8, m9), apebs[m] = mkpeb(aehdr, avidhdr(v, n, m0, m1, m5), buf, m2, boolvar), recs[v × n] = recovery-entry(m3, m4), apebs[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), m6 < m, m < # apebs, m6 < # apebs, m6 + 1 < # apebs, v × n ∈ 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 ⊦ m6 = m3, m6 = m, avhdr.vol × avhdr.leb = v × n, avhdr.vol × avhdr.leb ∈ recs[v × n, recovery-entry(m, m0)] ∧ m8 = m6

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 46:
# wlar = # apebs, wlar[m6] = wl-entry(m11, used), apebs[m6] = mkpeb(aehdr0, avhdr, buf0, m10, boolvar0), recs[v × n] = recovery-entry(m3, m4), apebs[m] = mkpeb(aehdr, avidhdr(v, n, m0, m1, m5), buf, m2, boolvar), recs[avhdr.vol × avhdr.leb] = recovery-entry(m8, m9), m6 + 1 < # apebs, m6 < # apebs, m < # apebs, m6 < m, v × n ∈ 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 ⊦ m6 = m, m6 = m3, avhdr.vol × avhdr.leb = v × n, avhdr.vol × avhdr.leb ∈ recs ∧ m8 = m6

Rule argument

Additional information

Used simplifier rules: ⊦ ladr ≠ ladr0 → (ladr ∈ recs[ladr0, rec] ↔ ladr ∈ recs); (s)% ⊦ ladr ≠ ladr0 → recs[ladr0, rec][ladr] = recs[ladr]; (s)