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Proof step 42 from proof mapped-pebs-unmap (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, 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, vols[v, vols[v][m, unmapped]][v0][m1] = ⌜n⌝ ∧ m1 < # vols[v, vols[v][m, unmapped]][v0]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 43:
⊦ v ≠ v0 → vols[v0, ebatbl][v] = vols[v]
Proof step 44:
vols[v][m] = ⌜n0⌝ , vols[v0][m1] = ⌜n⌝ , v0 = v, m < # vols[v], m1 < # vols[v0], v0 ∈ vols[v, vols[v][m, unmapped]], 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, unmapped]][v0][m1] = ⌜n⌝ ∧ m1 < # vols[v, vols[v][m, unmapped]][v0]

Rule argument

spec: store, inst: volumes name: At-other seq: ⊦ v ≠ v0 → vols[v0, ebatbl][v] = vols[v] subst: [v, ebatbl, v0, vols] → [v0, vols[v][m, unmapped], v, vols] flags: <all paths>

Additional information

Used simplifier rules: ⊦ v ≠ v0 → (v ∈ vols[v0, ebatbl] ↔ v ∈ vols); (s) Used terms: v0, vols[v][m, unmapped], v, vols