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Proof step 8 from proof valid-ebatbl-unmap (previous step)

apebs[n] = mkpeb(aehdr, avhdr, buf, m3, boolvar), vols[v][m] = ⌜n⌝ , wlar[n, wl-entry(m0, erasing)][n] = wl-entry(m2, stat), m < # vols[v], n < # wlar, 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 ⊦ vols[v, vols[v][m, unmapped]][v0][m1] = ⌜n⌝ ∧ v0 ∈ vols[v, vols[v][m, unmapped]] ∧ m1 < # vols[v, vols[v][m, unmapped]][v0] ↔ stat = used ∧ n < # apebs ∧ n < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v0 ∧ avhdr.leb = m1 ∧ n ≠ n0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
vols[v, vols[v][m, unmapped]][v0][m1] = ⌜n⌝ , vols[v][m] = ⌜n⌝ , apebs[n] = mkpeb(aehdr, avhdr, buf, m3, boolvar), m1 < # vols[v, vols[v][m, unmapped]][v0], n < # wlar, m < # vols[v], v0 ∈ vols[v, vols[v][m, unmapped]], 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 ⊦

Rule argument

Additional information

Used simplifier rules: ⊦ used ≠ erasing; (s)% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)% ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)