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Proof step 27 from proof mapped-pebs-unmap (previous step)

vols[v][m] = ⌜n0⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n0].status = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ apebs[n0].vidhdr.valid? ∧ apebs[n0].vidhdr.vol = v ∧ apebs[n0].vidhdr.leb = m ∧ n0 ≠ m0, vols[v][m] = ⌜n0⌝ , vols[v0][m1] = ⌜n⌝ , m < # vols[v], m1 < # vols[v0], v ∈ vols, v0 ∈ 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 ≠ m0 ⊦ v0 = v, n ≠ n0 ∧ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ )

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
wlar[n0].status = used, vols[v0][m1] = ⌜n⌝ , vols[apebs[n0].vidhdr.vol][apebs[n0].vidhdr.leb] = ⌜n0⌝ , apebs[n0].vidhdr.valid?, m1 < # vols[v0], n0 < # apebs, n0 < # wlar, apebs[n0].vidhdr.leb < # vols[apebs[n0].vidhdr.vol], v0 ∈ vols, apebs[n0].vidhdr.vol ∈ 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 ≠ m0 ⊦ n0 = m0, v0 = apebs[n0].vidhdr.vol, n ≠ n0 ∧ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ )

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic