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Proof step 5 from proof mapped-pebs-remap (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 ⊦ ∀ n. n ∈ mapped-pebs(vols[v, vols[v][m, ⌜n1⌝ ]]) ↔ n ∈ (mapped-pebs(vols) -- n0) ++ n1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
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 ⊦ (∃ v0, m0. v0 ∈ vols[v, vols[v][m, ⌜n1⌝ ]] ∧ m0 < # vols[v, vols[v][m, ⌜n1⌝ ]][v0] ∧ vols[v, vols[v][m, ⌜n1⌝ ]][v0][m0] = ⌜n⌝ ) ↔ n = n1 ∨ n ≠ n0 ∧ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ )

Rule argument

Additional information

Used simplifier rules: mapped-pebs: ⊦ n ∈ mapped-pebs(vols) ↔ (∃ v, m. v ∈ vols ∧ m < # vols[v] ∧ vols[v][m] = ⌜n⌝ );% ⊦ n ∈ ns -- n0 ↔ n ≠ n0 ∧ n ∈ ns; (s)% ⊦ n ∈ ns ++ n0 ↔ n = n0 ∨ n ∈ ns; (s)