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Proof step 42 from proof absexpt-pebs-write (previous step)

# vols[v0] = # avols[v0], 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, apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), vols[v][m] = ⌜n⌝ , apebs[n, apeb][n] = mkpeb(aehdr, avhdr, buf, m2, boolvar), avols[v0][m0] = mapped(buf0, m1), vols[v0][m0] = ⌜n⌝ , m < # vols[v], m0 < # avols[v0], v ∈ vols, v0 ∈ vols, v0 ∈ avols, m3 ≤ m1, ∀ 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, v0 ≠ v ∨ m0 ≠ m ⊦ buf0 = buf ∧ m2 ≤ m1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 43:
# vols[v0] = # avols[v0], wlar[n].status = used, vols[avhdr0.vol][avhdr0.leb] = ⌜n⌝ , apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), vols[v0][m0] = ⌜n⌝ , avols[v0][m0] = mapped(buf0, m1), avhdr0.valid?, m0 < # avols[v0], n < # apebs, n < # wlar, avhdr0.leb < # vols[avhdr0.vol], avhdr0.vol ∈ vols, v0 ∈ avols, v0 ∈ vols, m3 ≤ m1, ∀ 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, v0 ≠ avhdr0.vol ∨ m0 ≠ avhdr0.leb ⊦ n = n0, buf0 = buf ∧ m2 ≤ m1

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)% ⊦ mkpeb(aehdr, avhdr, buf, m, boolvar).vidhdr = avhdr; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%m < # apebs ⊦ apebs[m, apeb][m] = apeb; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)