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Proof step 10 from proof valid-ebatbl-update-vhdrs-unused (previous step)

vols[v][m1] = ⌜n0⌝ ∧ v ∈ vols ∧ m1 < # vols[v] ↔ stat0 = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ avhdr0.valid? ∧ avhdr0.vol = v ∧ avhdr0.leb = m1 ∧ n0 ≠ n, apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar[m] = wl-entry(m0, stat), wlar[n0] = wl-entry(m3, stat0), apebs[m, apeb][n0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), ∀ v, m1, n0. vols[v][m1] = ⌜n0⌝ ∧ v ∈ vols ∧ m1 < # vols[v] ↔ wlar[n0].status = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ apebs[m, apeb][n0].vidhdr.valid? ∧ apebs[m, apeb][n0].vidhdr.vol = v ∧ apebs[m, apeb][n0].vidhdr.leb = m1 ∧ n0 ≠ n ⊦ vols[v][m1] = ⌜n0⌝ ∧ v ∈ vols ∧ m1 < # vols[v] ↔ stat0 = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v ∧ avhdr.leb = m1 ∧ n0 ≠ n, stat = used

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: n0 = m

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)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws) Used formulas: n0 = m