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Proof step 8 from proof valid-wl-markbad (previous step)

# apebs = # wlar, wlar[n] = wl-entry(m5, stat), apebs[n] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar), apebs[m, mkpeb(aehdr, avhdr, buf, m0, true)][n] = mkpeb(aehdr1, avhdr1, buf1, m4, boolvar0), wlar[m, wl-entry(m1, erroneous)][n] = wl-entry(m6, stat0), m < # wlar, n < # wlar, ∀ n. n < # wlar → (wlar[n].status = erroneous ↔ apebs[n].bad) ∧ (wlar[n].status = free → apebs[n].vidhdr = empty) ∧ (wlar[n].status ≠ erroneous ∧ wlar[n].status ≠ erasing → apebs[n].echdr = aechdr(wlar[n].ec)) ∧ (wlar[n].status = used → (∃ v, m. valid-peb(v, m, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m, apebs).max)) ⊦ (stat0 = erroneous ↔ boolvar0) ∧ (stat0 = free → avhdr0 = empty) ∧ (stat0 ≠ erroneous ∧ stat ≠ erasing → aehdr0 = aechdr(m5)) ∧ ( stat0 = used → (∃ v, m2. valid-peb(v, m2, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar)) ∧ avhdr0.sqn = valid-sqns(v, m2, apebs[m, mkpeb(aehdr, avhdr, buf, m0, true)]).max))

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Rule argument

fma: n = m

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # apebs ⊦ apebs[m, apeb][m] = apeb; (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 < # wlar → wlar[m, wle][m] = wle; (s)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)% ⊦ free ≠ erroneous; (s)% ⊦ used ≠ erroneous; (s) Used formulas: n = m