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Proof step 27 from proof valid-ebatbl-remap (previous step)

wlar[n] = wl-entry(m9, stat0), apebs[n1] = mkpeb(aehdr0, avhdr, buf0, m7, boolvar0), apebs[n] = mkpeb(aehdr, avidhdr(v0, m2, m3, m4, m5), buf, m6, boolvar), vols[v0][m2] = ⌜n1⌝ , vols[v0, vols[v0][m2, ⌜n⌝ ]][v][m] = ⌜n1⌝ , n1 < # wlar, n < # wlar, n < # apebs, m2 < # vols[v0], m < # vols[v0, vols[v0][m2, ⌜n⌝ ]][v], v0 ∈ vols, v ∈ vols[v0, vols[v0][m2, ⌜n⌝ ]], ∀ 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, n1 = n0, stat0 = used, v = v0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
vols[v][m] = ⌜n1⌝ , wlar[n] = wl-entry(m9, stat0), apebs[n1] = mkpeb(aehdr0, avhdr, buf0, m7, boolvar0), apebs[n] = mkpeb(aehdr, avidhdr(v0, m2, m3, m4, m5), buf, m6, boolvar), vols[v0][m2] = ⌜n1⌝ , m < # vols[v], n1 < # wlar, n < # wlar, n < # apebs, m2 < # vols[v0], v0 ∈ vols, v ∈ vols, ∀ 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, n1 = n0, stat0 = used, v = v0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ v ≠ v0 → (v ∈ vols[v0, ebatbl] ↔ v ∈ vols); (s)% ⊦ v ≠ v0 → vols[v0, ebatbl][v] = vols[v]; (s)