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Proof step 2 from proof valid-ebatbl-map (previous step)

apebs[n].vidhdr.leb = m, apebs[n].vidhdr.vol = v, vols[v][m] = unmapped, apebs[n].vidhdr.valid?, m < # vols[v], n < # apebs, n < # wlar, v ∈ vols ⊦ wlar[n].status = used, valid-ebatbl(apebs, wlar[n, wl-entry(m0, used)], vols[v, vols[v][m, ⌜n⌝ ]], n0) ↔ valid-ebatbl(apebs, wlar, vols, n0), n = n0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
vols[apebs[n].vidhdr.vol][apebs[n].vidhdr.leb] = unmapped, apebs[n].vidhdr.valid?, apebs[n].vidhdr.leb < # vols[apebs[n].vidhdr.vol], n < # apebs, n < # wlar, apebs[n].vidhdr.vol ∈ vols ⊦ wlar[n].status = used, (∀ v, m, n1. vols[apebs[n].vidhdr.vol, vols[apebs[n].vidhdr.vol][apebs[n].vidhdr.leb, ⌜n⌝ ]][v][m] = ⌜n1⌝ ∧ v ∈ vols[apebs[n].vidhdr.vol, vols[apebs[n].vidhdr.vol][apebs[n].vidhdr.leb, ⌜n⌝ ]] ∧ m < # vols[apebs[n].vidhdr.vol, vols[apebs[n].vidhdr.vol][apebs[n].vidhdr.leb, ⌜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: valid-ebatbl: ⊦ valid-ebatbl(apebs, wlar, vols, n0) ↔ (∀ v, m, n. vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n].status = used ∧ n < # apebs ∧ n < # wlar ∧ apebs[n].vidhdr.valid? ∧ apebs[n].vidhdr.vol = v ∧ apebs[n].vidhdr.leb = m ∧ n ≠ n0);% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # wlar[n, wle] = # wlar; (s)