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Proof step 10 from proof valid-ebatbl-write-data (previous step)

vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ stat = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ avhdr1.valid? ∧ avhdr1.vol = v ∧ avhdr1.leb = m ∧ n1 ≠ n0, apebs[n1] = mkpeb(aehdr0, avhdr0, buf, m2, boolvar0), apebs[n] = mkpeb(aehdr, avhdr, buf0, m0, boolvar), wlar[n1] = wl-entry(m3, stat), apebs[n, mkpeb(aehdr, avhdr, buf1, m1, boolvar)][n1] = mkpeb(aehdr1, avhdr1, buf2, m4, boolvar1), ∀ v, m, n1. vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ wlar[n1].status = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ apebs[n, mkpeb(aehdr, avhdr, buf1, m1, boolvar)][n1].vidhdr.valid? ∧ apebs[n, mkpeb(aehdr, avhdr, buf1, m1, boolvar)][n1].vidhdr.vol = v ∧ apebs[n, mkpeb(aehdr, avhdr, buf1, m1, boolvar)][n1].vidhdr.leb = m ∧ n1 ≠ n0 ⊦ vols[v][m] = ⌜n1⌝ ∧ v ∈ vols ∧ m < # vols[v] ↔ stat = used ∧ n1 < # apebs ∧ n1 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m ∧ n1 ≠ n0

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: n1 = n

Additional information

Used simplifier rules: ⊦ m ≠ n → apebs[n, apeb][m] = apebs[m]; (s)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%m < # apebs ⊦ apebs[m, apeb][m] = apeb; (s) Used formulas: n1 = n