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Proof step 9 from proof valid-wl-next-valid-erase (previous step)

# apebs = # wlar, wlar[n0] = wl-entry(m4, stat), apebs[m] = mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0), apebs[n0] = mkpeb(aehdr, avhdr, buf, m2, boolvar), wlar[m, wl-entry(m0, erasing)][n0] = wl-entry(m5, stat0), n0 < # wlar, m < # wlar, valid-peb(v, n, mkpeb(aehdr0, avhdr0, buf0, m3, boolvar0)), n0 ≤ m, valid-sqns(v, n, apebs, m) ≠ ∅ → avhdr0.sqn < valid-sqns(v, n, apebs, m).max, ∀ n0. n0 < m → (wlar[n0].status = erroneous ↔ apebs[n0].bad) ∧ (wlar[n0].status = free → apebs[n0].vidhdr = empty) ∧ (wlar[n0].status ≠ erroneous ∧ wlar[n0].status ≠ erasing → apebs[n0].echdr = aechdr(wlar[n0].ec)) ∧ (wlar[n0].status = used → (∃ v0, m1. valid-peb(v0, m1, apebs[n0]) ∧ apebs[n0].vidhdr.sqn = valid-sqns(v0, m1, apebs, m).max)) ⊦ (stat0 = erroneous ↔ boolvar) ∧ (stat0 = free → avhdr = empty) ∧ (stat ≠ erroneous ∧ stat0 ≠ erasing → aehdr = aechdr(m4)) ∧ ( stat0 = used → (∃ v0, m1. valid-peb(v0, m1, mkpeb(aehdr, avhdr, buf, m2, stat = erroneous)) ∧ avhdr.sqn = (valid-sqns(v0, m1, apebs, m) ∪ (v = v0 ∧ n = m1 ⊃ {avhdr0.sqn} ;∅)).max))

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Rule argument

fma: n0 = 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)% ⊦ m ≤ m; (s)%⊦ mkpeb(aehdr, avhdr, buf, m, boolvar) = mkpeb(aehdr0, avhdr0, buf0, m0, boolvar0) ↔ aehdr = aehdr0 ∧ avhdr = avhdr0 ∧ buf = buf0 ∧ m = m0 ∧ (boolvar ↔ boolvar0); (s)% ⊦ ¬ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, true)); (s)% ⊦ erroneous ≠ erasing; (s)% ⊦ free ≠ erasing; (s)% ⊦ used ≠ erasing; (s) Used formulas: n0 = m