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Proof step 7 from proof lf-valid-recs-max (previous step)

# apebs = # wlar, recs[v × n] = recovery-entry(m0, avhdr.sqn), apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), m0 < # wlar, m0 < m, valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, m), subarray(wlar, 0, m)), v × n ∈ recs, m ≤ # wlar, ∀ ladr, m0. ladr ∈ recs ∧ recs[ladr].pnum = m0 ↔ subarray(wlar, 0, m)[m0].status = used ∧ m0 < # subarray(apebs, 0, m) ∧ subarray(apebs, 0, m)[m0].vidhdr.vol = ladr.vol ∧ subarray(apebs, 0, m)[m0].vidhdr.leb = ladr.leb ⊦ avhdr.sqn = valid-sqns(v, n, apebs, m).max

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
# apebs = # wlar, apebs[m0] = mkpeb(aehdr, avhdr, buf, m1, boolvar), recs[v × n] = recovery-entry(m0, avhdr.sqn), m0 < m, m0 < # wlar, valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m1, boolvar)), valid-recs-sqns(apebs, recs), valid-wl(subarray(apebs, 0, m), subarray(wlar, 0, m)), v × n ∈ recs, m ≤ # wlar, ∀ ladr, m2. ladr ∈ recs ∧ recs[ladr].pnum = m2 ↔ wlar[m2].status = used ∧ m2 < m ∧ apebs[m2].vidhdr.vol = ladr.vol ∧ apebs[m2].vidhdr.leb = ladr.leb ⊦ avhdr.sqn = valid-sqns(v, n, apebs, m).max

Rule argument

Additional information

Used simplifier rules: ⊦ n0 < n → subarray(wlar, m, n)[n0] = wlar[m + n0]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n0 < n → subarray(apebs, m, n)[n0] = apebs[m + n0]; (s)% ⊦ # subarray(apebs, m, n) = n; (s)