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Proof step 5 from proof lf-valid-recs-valid-peb (previous step)

# apebs = # wlar, recs[v × m] = recovery-entry(n0, n1), n0 < # wlar, n0 < m0, valid-wl(subarray(apebs, 0, m0), subarray(wlar, 0, m0)), v × m ∈ recs, m0 ≤ # wlar, ∀ ladr, m. ladr ∈ recs ∧ recs[ladr].pnum = m ↔ subarray(wlar, 0, m0)[m].status = used ∧ m < # subarray(apebs, 0, m0) ∧ subarray(apebs, 0, m0)[m].vidhdr.vol = ladr.vol ∧ subarray(apebs, 0, m0)[m].vidhdr.leb = ladr.leb ⊦ valid-peb(v, m, apebs[n0])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
# apebs = # wlar, recs[v × m] = recovery-entry(n0, n1), n0 < m0, n0 < # wlar, valid-wl(subarray(apebs, 0, m0), subarray(wlar, 0, m0)), v × m ∈ recs, m0 ≤ # wlar, ∀ ladr, m1. ladr ∈ recs ∧ recs[ladr].pnum = m1 ↔ wlar[m1].status = used ∧ m1 < m0 ∧ apebs[m1].vidhdr.vol = ladr.vol ∧ apebs[m1].vidhdr.leb = ladr.leb ⊦ valid-peb(v, m, apebs[n0])

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)