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Proof step 51 from proof mapped-pebs-remap (previous step)

vols[v0][m1] = ⌜n⌝ , vols[v][m] = ⌜n0⌝ , m1 < # vols[v0], m < # vols[v], v0 ∈ vols, v ∈ vols, v0 ∈ vols[v, vols[v][m, ⌜n1⌝ ]], ∀ 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, vols[v, vols[v][m, ⌜n1⌝ ]][v0][m1] = ⌜n⌝ ∧ m1 < # vols[v, vols[v][m, ⌜n1⌝ ]][v0]

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 52:
vols[v][m] = ⌜n0⌝ , vols[v0][m1] = ⌜n⌝ , v0 = v, m < # vols[v], m1 < # vols[v0], v0 ∈ vols[v, vols[v][m, ⌜n1⌝ ]], 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, vols[v, vols[v][m, ⌜n1⌝ ]][v0][m1] = ⌜n⌝ ∧ m1 < # vols[v, vols[v][m, ⌜n1⌝ ]][v0]

Rule argument

fma: v0 = v

Additional information

Used simplifier rules: ⊦ v ≠ v0 → (v ∈ vols[v0, ebatbl] ↔ v ∈ vols); (s)% ⊦ v ≠ v0 → vols[v0, ebatbl][v] = vols[v]; (s) Used formulas: v0 = v