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Proof step 41 from proof valid-ebatbl-remap (previous step)

wlar[n, wl-entry(m0, used)][n2] = wl-entry(m8, stat), wlar[n] = wl-entry(m9, stat0), apebs[n2] = mkpeb(aehdr0, avhdr, buf0, m7, boolvar0), apebs[n] = mkpeb(aehdr, avidhdr(v0, m2, m3, m4, m5), buf, m6, boolvar), vols[v0][m2] = ⌜n1⌝ , n2 = n, n < # wlar, n < # apebs, m2 < # vols[v0], v0 ∈ vols, ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0 ⊦ vols[v0, vols[v0][m2, ⌜n⌝ ]][v][m] = ⌜n2⌝ ∧ v ∈ vols[v0, vols[v0][m2, ⌜n⌝ ]] ∧ m < # vols[v0, vols[v0][m2, ⌜n⌝ ]][v] ↔ stat = used ∧ n2 < # apebs ∧ n2 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v ∧ avhdr.leb = m ∧ n2 ≠ n0, n = n0, n1 = n0, n2 = n1, stat0 = used

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
vols[v0, vols[v0][m2, ⌜n⌝ ]][v][m] = ⌜n⌝ , vols[v0][m2] = ⌜n1⌝ , wlar[n] = wl-entry(m9, stat0), apebs[n] = mkpeb(aehdr0, avidhdr(v0, m2, m3, m4, m5), buf0, m7, boolvar0), m < # vols[v0, vols[v0][m2, ⌜n⌝ ]][v], n < # wlar, n < # apebs, m2 < # vols[v0], v ∈ vols[v0, vols[v0][m2, ⌜n⌝ ]], v0 ∈ vols, ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n1].vidhdr.valid? ∧ apebs[n1].vidhdr.vol = v ∧ apebs[n1].vidhdr.leb = m ∧ n1 ≠ n0 ⊦ n = n0, n = n1, n1 = n0, stat0 = used, v0 = v ∧ m2 = m

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ # ebatbl[n, ebae] = # ebatbl; (s)% ⊦ v ∈ vols[v, ebatbl]; (s)% ⊦ ⌜m⌝ = ⌜m0⌝ ↔ m = m0; (s)%m < # ebatbl ⊦ ebatbl[m, ebae][m] = ebae; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ vols[v, ebatbl][v] = 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)%⊦ 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)