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Proof step 30 from proof valid-ebatbl-map (previous step)

vols[v0, vols[v0][m1, ⌜n⌝ ]][v][m] = ⌜n⌝ , wlar[n] = wl-entry(m6, stat), apebs[n] = mkpeb(aehdr0, avidhdr(v0, m1, m2, m3, m4), buf0, m7, boolvar0), vols[v0][m1] = unmapped, m < # vols[v0, vols[v0][m1, ⌜n⌝ ]][v], n < # wlar, n < # apebs, m1 < # vols[v0], v ∈ vols[v0, vols[v0][m1, ⌜n⌝ ]], v0 ∈ vols ⊦ n = n0, stat = used, v0 = v ∧ m1 = m, vols[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v]

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: v = v0

Additional information

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