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Proof step 17 from proof valid-ebatbl-map (previous step)

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

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)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ unmapped ≠ ⌜m⌝ ; (s) Used formulas: v = v0