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

vols[v][m2] = ⌜n0⌝ ∧ v ∈ vols ∧ m2 < # vols[v] ↔ stat2 = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v ∧ avhdr.leb = m2 ∧ n0 ≠ n, apebs[n0] = mkpeb(aehdr, avhdr, buf, m3, boolvar), wlar[m] = wl-entry(m0, stat), wlar[n0] = wl-entry(m4, stat1), wlar[m, wl-entry(m1, stat0)][n0] = wl-entry(m5, stat2), ∀ v, m2, n0. vols[v][m2] = ⌜n0⌝ ∧ v ∈ vols ∧ m2 < # vols[v] ↔ wlar[m, wl-entry(m1, stat0)][n0].status = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ apebs[n0].vidhdr.valid? ∧ apebs[n0].vidhdr.vol = v ∧ apebs[n0].vidhdr.leb = m2 ∧ n0 ≠ n ⊦ vols[v][m2] = ⌜n0⌝ ∧ v ∈ vols ∧ m2 < # vols[v] ↔ stat1 = used ∧ n0 < # apebs ∧ n0 < # wlar ∧ avhdr.valid? ∧ avhdr.vol = v ∧ avhdr.leb = m2 ∧ n0 ≠ n, stat = used, stat0 = used

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: n0 = m

Additional information

Used simplifier rules: ⊦ m ≠ n → wlar[n, wle][m] = wlar[m]; (s)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n < m ↔ false); (s)%m < # wlar ⊦ wlar[m, wle][m] = wle; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic Used formulas: n0 = m