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Proof step 19 from proof valid-ebatbl-map (previous step)

vols[v0, vols[v0][m1, ⌜n⌝ ]][v][m] = ⌜n1⌝ ∧ v ∈ vols[v0, vols[v0][m1, ⌜n⌝ ]] ∧ m < # vols[v0, vols[v0][m1, ⌜n⌝ ]][v] ↔ stat0 = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v ∧ avhdr.leb = m ∧ n1 ≠ n0, wlar[n1] = wl-entry(m8, stat0), apebs[n1] = mkpeb(aehdr0, avhdr, buf0, m7, boolvar0), vols[v0][m1] = unmapped, apebs[n] = mkpeb(aehdr, avidhdr(v0, m1, m2, m3, m4), buf, m5, boolvar), wlar[n] = wl-entry(m6, stat), m1 < # vols[v0], n < # apebs, n < # wlar, v0 ∈ vols ⊦ vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ stat0 = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v ∧ avhdr.leb = m ∧ n1 ≠ n0, n = n0, n1 = n, stat = used

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 20:
vols[v0, vols[v0][m1, ⌜n⌝ ]][v][m] = ⌜n1⌝ ∧ v ∈ vols[v0, vols[v0][m1, ⌜n⌝ ]] ∧ m < # vols[v0, vols[v0][m1, ⌜n⌝ ]][v] ↔ stat0 = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v ∧ avhdr.leb = m ∧ n1 ≠ n0, wlar[n] = wl-entry(m6, stat), apebs[n] = mkpeb(aehdr, avidhdr(v0, m1, m2, m3, m4), buf, m5, boolvar), vols[v0][m1] = unmapped, apebs[n1] = mkpeb(aehdr0, avhdr, buf0, m7, boolvar0), wlar[n1] = wl-entry(m8, stat0), v = v0, n < # wlar, n < # apebs, m1 < # vols[v0], v0 ∈ vols ⊦ vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ stat0 = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v ∧ avhdr.leb = m ∧ n1 ≠ n0, n = n0, n1 = n, stat = used

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) Used formulas: v = v0