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

apebs[n] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar[m] = wl-entry(m0, stat), wlar[n] = wl-entry(m4, stat0), wlar[m, wl-entry(m1, erasing)][n] = wl-entry(m5, stat1), 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)) ⊦ stat = erroneous, (stat1 = erroneous ↔ boolvar) ∧ (stat1 = free → avhdr = empty) ∧ (stat0 ≠ erroneous ∧ stat1 ≠ erasing → aehdr = aechdr(m4)) ∧ (stat1 = used → (∃ v, m3. valid-peb(v, m3, mkpeb(aehdr, avhdr, buf, m2, stat0 = erroneous)) ∧ avhdr.sqn = valid-sqns(v, m3, apebs).max))

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 9:
wlar[m, wl-entry(m1, erasing)][n] = wl-entry(m5, stat1), wlar[n] = wl-entry(m4, stat0), wlar[m] = wl-entry(m0, stat), apebs[n] = mkpeb(aehdr, avhdr, buf, m2, boolvar), n = m, 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)) ⊦ stat = erroneous, (stat1 = erroneous ↔ boolvar) ∧ (stat1 = free → avhdr = empty) ∧ (stat0 ≠ erroneous ∧ stat1 ≠ erasing → aehdr = aechdr(m4)) ∧ (stat1 = used → (∃ v, m3. valid-peb(v, m3, mkpeb(aehdr, avhdr, buf, m2, stat0 = erroneous)) ∧ avhdr.sqn = valid-sqns(v, m3, apebs).max))
Proof step 11:
wlar[m, wl-entry(m1, erasing)][n] = wl-entry(m5, stat1), wlar[n] = wl-entry(m4, stat0), wlar[m] = wl-entry(m0, stat), apebs[n] = mkpeb(aehdr, avhdr, buf, m2, boolvar), 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)) ⊦ n = m, stat = erroneous, (stat1 = erroneous ↔ boolvar) ∧ (stat1 = free → avhdr = empty) ∧ (stat0 ≠ erroneous ∧ stat1 ≠ erasing → aehdr = aechdr(m4)) ∧ (stat1 = used → (∃ v, m3. valid-peb(v, m3, mkpeb(aehdr, avhdr, buf, m2, stat0 = erroneous)) ∧ avhdr.sqn = valid-sqns(v, m3, apebs).max))

Rule argument

fma: n = m

Additional information

Used formulas: n = m