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Proof step 39 from proof mapped-pebs-unmap (previous step)

vols[v][m] = ⌜n0⌝ , m < # vols[v], 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 ≠ m0, ∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ ⊦ n = n0, ∃ v0, m0. v0 ∈ vols[v, vols[v][m, unmapped]] ∧ m0 < # vols[v, vols[v][m, unmapped]][v0] ∧ vols[v, vols[v][m, unmapped]][v0][m0] = ⌜n⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
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 ⊦ n = n0, ∃ v0, m0. v0 ∈ vols[v, vols[v][m, unmapped]] ∧ m0 < # vols[v, vols[v][m, unmapped]][v0] ∧ vols[v, vols[v][m, unmapped]][v0][m0] = ⌜n⌝

Rule argument

Additional information

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