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Proof step 15 from proof valid-wl-free (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 16:
apebs[n] = mkpeb(aehdr, avhdr, buf0, m2, boolvar), apebs[m] = mkpeb(aechdr(m1), empty, buf, m0, false), wlar[m, wl-entry(m1, free)][n] = wl-entry(m4, stat), n < # wlar, m < # 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 ↔ boolvar) ∧ (stat = free → avhdr = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr = aechdr(m4)) ∧ (stat = used → (∃ v, m3. valid-peb(v, m3, mkpeb(aehdr, avhdr, buf0, m2, wlar[n].status = erroneous)) ∧ avhdr.sqn = valid-sqns(v, m3, apebs).max))

Rule argument

fma: n = m

Additional information

Used simplifier rules: ⊦ m < # wlar → wlar[m, wle][m] = wle; (s)% ⊦ wl-entry(m, stat) = wl-entry(m0, stat0) ↔ m = m0 ∧ stat = stat0; (ws)% ⊦ ¬ valid-peb(v, m, mkpeb(aehdr, empty, buf, m0, boolvar)); (s)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s)% ⊦ free ≠ erroneous; (s)% ⊦ free ≠ erasing; (s)% ⊦ used ≠ free; (s) Used formulas: n = m