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Proof step 16 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] ↔ stat1 = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v ∧ avhdr.leb = m ∧ n1 ≠ n0, wlar[n, wl-entry(m0, used)][n1] = wl-entry(m9, stat1), wlar[n1] = wl-entry(m8, stat0), 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), n1 = n, 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, stat = used

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
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

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)% ⊦ v ∈ vols → vols[v, vols[v]] = vols; (s)% ⊦ ebatbl[n] = ebae → ebatbl[n, ebae] = ebatbl; (s)% ⊦ avidhdr(v, m, m0, m1, m2).leb = m; (s)% ⊦ avidhdr(v, m, m0, m1, m2).vol = v; (s)% ⊦ avidhdr(v, m, m0, m1, m2).valid?; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)% ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)