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Proof step 17 from proof valid-wl-next-free (previous step)

# apebs = # wlar, apebs[m] = mkpeb(aechdr(m0), empty, buf, m1, false), apebs[n] = mkpeb(aehdr, avhdr, buf0, m3, false), wlar[n] = wl-entry(m4, stat), n + 1 < # wlar, n < # wlar, m < # wlar, n < m, ∀ n. n < m → (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, m2. valid-peb(v, m2, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m2, apebs, m).max)) ⊦ n = m, stat = erasing, stat = erroneous, (stat = free → avhdr = empty) ∧ aehdr = aechdr(m4) ∧ (stat = used → (∃ v, m2. valid-peb(v, m2, mkpeb(aechdr(m4), avhdr, buf0, m3, false)) ∧ avhdr.sqn = valid-sqns(v, m2, apebs, m).max))

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 18:
# apebs = # wlar, wlar[n] = wl-entry(m4, stat), apebs[n] = mkpeb(aehdr, avhdr, buf0, m3, false), apebs[m] = mkpeb(aechdr(m0), empty, buf, m1, false), stat = free, n < m, m < # wlar, n < # wlar, n + 1 < # wlar, ∀ n. n < m → (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, m2. valid-peb(v, m2, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m2, apebs, m).max)) ⊦ n = m, stat = erroneous, stat = erasing, (stat = free → avhdr = empty) ∧ aehdr = aechdr(m4) ∧ (stat = used → (∃ v, m2. valid-peb(v, m2, mkpeb(aechdr(m4), avhdr, buf0, m3, false)) ∧ avhdr.sqn = valid-sqns(v, m2, apebs, m).max))
Proof step 24:
# apebs = # wlar, wlar[n] = wl-entry(m4, stat), apebs[n] = mkpeb(aehdr, avhdr, buf0, m3, false), apebs[m] = mkpeb(aechdr(m0), empty, buf, m1, false), n < m, m < # wlar, n < # wlar, n + 1 < # wlar, ∀ n. n < m → (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, m2. valid-peb(v, m2, apebs[n]) ∧ apebs[n].vidhdr.sqn = valid-sqns(v, m2, apebs, m).max)) ⊦ n = m, stat = erroneous, stat = erasing, stat = free, (stat = free → avhdr = empty) ∧ aehdr = aechdr(m4) ∧ (stat = used → (∃ v, m2. valid-peb(v, m2, mkpeb(aechdr(m4), avhdr, buf0, m3, false)) ∧ avhdr.sqn = valid-sqns(v, m2, apebs, m).max))

Rule argument

fma: stat = free

Additional information

Used formulas: stat = free