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Proof step 4 from proof valid-ebatbl-map (previous step)

apebs[n].vidhdr = avidhdr(v0, m1, m2, m3, m4), vols[v0][m1] = unmapped, apebs[n].vidhdr.valid?, n < # wlar, n < # apebs, m1 < # vols[v0], v0 ∈ vols ⊦ wlar[n].status = used, (∀ v, m, n1. vols[v0, vols[v0][m1, ⌜n⌝ ]][v][m] = ⌜n1⌝ ∧ v ∈ vols[v0, vols[v0][m1, ⌜n⌝ ]] ∧ m < # vols[v0, vols[v0][m1, ⌜n⌝ ]][v] ↔ wlar[n, wl-entry(m0, used)][n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0) ↔ (∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0), n = n0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
apebs[n].vidhdr = avidhdr(v0, m1, m2, m3, m4), vols[v0][m1] = unmapped, n < # wlar, n < # apebs, m1 < # vols[v0], v0 ∈ vols ⊦ wlar[n].status = used, (∀ v, m, n1. vols[v0, vols[v0][m1, ⌜n⌝ ]][v][m] = ⌜n1⌝ ∧ v ∈ vols[v0, vols[v0][m1, ⌜n⌝ ]] ∧ m < # vols[v0, vols[v0][m1, ⌜n⌝ ]][v] ↔ wlar[n, wl-entry(m0, used)][n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0) ↔ (∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0), n = n0

Rule argument

Additional information

Used simplifier rules: ⊦ avidhdr(v, m, m0, m1, m2).valid?; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic