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Proof step 8 from proof mapped-pebs-unmap (previous step)

vols[v][m] = ⌜n0⌝ , vols[v, vols[v][m, unmapped]][v0][m1] = ⌜n⌝ , m < # vols[v], m1 < # vols[v, vols[v][m, unmapped]][v0], v ∈ vols, v0 ∈ vols[v, vols[v][m, unmapped]], ∀ 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 ∧ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ )

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 9:
vols[v, vols[v][m, unmapped]][v0][m1] = ⌜n⌝ , vols[v][m] = ⌜n0⌝ , v0 = v, m1 < # vols[v, vols[v][m, unmapped]][v0], 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 ≠ m0 ⊦ n ≠ n0 ∧ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ )
Proof step 25:
vols[v, vols[v][m, unmapped]][v0][m1] = ⌜n⌝ , vols[v][m] = ⌜n0⌝ , m1 < # vols[v, vols[v][m, unmapped]][v0], 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 ≠ m0 ⊦ v0 = v, n ≠ n0 ∧ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ )

Rule argument

fma: v0 = v

Additional information

Used formulas: v0 = v