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Proof step 11 from proof valid-wl-next-valid-update (previous step)

# apebs = # wlar, avhdr0.sqn = valid-sqns(v, n, apebs, m).max, wlar[m, wl-entry(aehdr.ec, used)][m0, wl-entry(m1, erasing)][n0] = wl-entry(m6, stat), apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), apebs[m] = mkpeb(aehdr, avhdr, buf, m3, boolvar), apebs[n0] = mkpeb(aehdr1, avhdr1, buf1, m5, boolvar1), m0 < # wlar, m < # wlar, avhdr0.sqn < avhdr.sqn, m0 < m, n0 < # wlar, m0 + 1 < # wlar, valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m3, boolvar)), valid-peb(v, n, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)), n0 ≤ m, ∀ v, m. unique-elems(valid-sqns(v, m, apebs)), ∀ 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, m2. valid-peb(v0, m2, apebs[n0]) ∧ apebs[n0].vidhdr.sqn = valid-sqns(v0, m2, apebs, m).max)) ⊦ (stat = erroneous ↔ boolvar1) ∧ (stat = free → avhdr1 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr1 = aechdr(m6)) ∧ ( stat = used → (∃ v0, m2. valid-peb(v0, m2, mkpeb(aehdr1, avhdr1, buf1, m5, false)) ∧ avhdr1.sqn = (valid-sqns(v0, m2, apebs, m) ∪ (v = v0 ∧ n = m2 ⊃ {avhdr.sqn} ;∅)).max))

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 12:
# apebs = # wlar, avhdr0.sqn = valid-sqns(v, n, apebs, m).max, apebs[n0] = mkpeb(aehdr1, avhdr1, buf1, m5, boolvar1), apebs[m] = mkpeb(aehdr, avhdr, buf, m3, boolvar), apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), wlar[m, wl-entry(aehdr.ec, used)][m0, wl-entry(m1, erasing)][n0] = wl-entry(m6, stat), m0 + 1 < # wlar, n0 < # wlar, m0 < m, avhdr0.sqn < avhdr.sqn, m < # wlar, m0 < # wlar, valid-peb(v, n, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)), valid-peb(v, n, mkpeb(aehdr, avhdr, buf, m3, boolvar)), n0 ≤ m, ∀ 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, m2. valid-peb(v0, m2, apebs[n0]) ∧ apebs[n0].vidhdr.sqn = valid-sqns(v0, m2, apebs, m).max)), ∀ v, m. unique-elems(valid-sqns(v, m, apebs)) ⊦ n0 = m0, (stat = erroneous ↔ boolvar1) ∧ (stat = free → avhdr1 = empty) ∧ (stat ≠ erroneous ∧ stat ≠ erasing → aehdr1 = aechdr(m6)) ∧ ( stat = used → (∃ v0, m2. valid-peb(v0, m2, mkpeb(aehdr1, avhdr1, buf1, m5, false)) ∧ avhdr1.sqn = (valid-sqns(v0, m2, apebs, m) ∪ (v = v0 ∧ n = m2 ⊃ {avhdr.sqn} ;∅)).max))

Rule argument

fma: n0 = m0

Additional information

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