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Proof step 33 from proof valid-ebatbl-map (previous step)

vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ stat1 = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v ∧ avhdr.leb = m ∧ n1 ≠ n0, wlar[n1] = wl-entry(m9, stat1), 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), v = v0, n < # wlar, n < # apebs, m1 < # vols[v0], v0 ∈ vols ⊦ vols[v0, vols[v0][m1, ⌜n⌝ ]][v][m] = ⌜n1⌝ ∧ v ∈ vols[v0, vols[v0][m1, ⌜n⌝ ]] ∧ m < # vols[v0, vols[v0][m1, ⌜n⌝ ]][v] ↔ vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v], n = n0, n1 = n, stat = used

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 34:
vols[v0][m] = ⌜n1⌝ ↔ stat1 = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v0 ∧ avhdr.leb = m ∧ n1 ≠ n0, 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), wlar[n1] = wl-entry(m9, stat1), m1 < # vols[v0], n < # apebs, n < # wlar, m < # vols[v0], v0 ∈ vols ⊦ vols[v0][m1, ⌜n⌝ ][m] = ⌜n1⌝ ↔ vols[v0][m] = ⌜n1⌝ , n = n0, n1 = n, stat = used

Rule argument

Additional information

Used simplifier rules: ⊦ # ebatbl[n, ebae] = # ebatbl; (s)% ⊦ v ∈ vols[v, ebatbl]; (s)% ⊦ vols[v, ebatbl][v] = ebatbl; (s)