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Proof step 17 from proof valid-ebatbl-write-data (previous step)

wlar[n] = wl-entry(m3, stat), apebs[n] = mkpeb(aehdr, avhdr, buf0, m0, boolvar), apebs[n, mkpeb(aehdr, avhdr, buf1, m1, boolvar)][n] = mkpeb(aehdr0, avhdr0, buf, m2, boolvar0), n < # apebs, ∀ 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[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ stat = used ∧ n < # apebs ∧ n < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m ∧ n ≠ n0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
wlar[n] = wl-entry(m3, stat), apebs[n] = mkpeb(aehdr, avhdr0, buf0, m0, boolvar), n < # apebs, ∀ 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[v][m] = ⌜n⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ stat = used ∧ n < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m ∧ n ≠ n0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (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)% ⊦ m < # apebs → apebs[m, apeb][m] = apeb; (s)