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Proof step 28 from proof valid-wl-next-valid-update (previous step)

# apebs = # wlar, avhdr1.sqn = valid-sqns(v0, m1, apebs, m).max, avhdr0.sqn = valid-sqns(v0, n, apebs, m).max, wlar[n0] = wl-entry(m7, used), apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), apebs[m] = mkpeb(aehdr, avhdr, buf, m3, boolvar), apebs[n0] = mkpeb(aechdr(m7), avhdr1, buf1, m5, false), n0 < m, m0 < # wlar, m < # wlar, avhdr0.sqn < avhdr.sqn, m0 < m, n0 < # wlar, m0 + 1 < # wlar, n0 + 1 < # wlar, valid-peb(v0, m1, mkpeb(aechdr(m7), avhdr1, buf1, m5, false)), valid-peb(v0, n, mkpeb(aehdr, avhdr, buf, m3, boolvar)), valid-peb(v0, n, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)), ∀ v, m. unique-elems(valid-sqns(v, m, apebs)) ⊦ avhdr1.sqn = (valid-sqns(v0, m1, apebs, m) ∪ (n = m1 ⊃ {avhdr.sqn} ;∅)).max, n0 = m0, n0 = m

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 29:
# apebs = # wlar, avhdr0.sqn = valid-sqns(v0, n, apebs, m).max, avhdr1.sqn = valid-sqns(v0, m1, apebs, m).max, apebs[n0] = mkpeb(aechdr(m7), avhdr1, buf1, m5, false), apebs[m] = mkpeb(aehdr, avhdr, buf, m3, boolvar), apebs[m0] = mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0), wlar[n0] = wl-entry(m7, used), n = m1, n0 + 1 < # wlar, m0 + 1 < # wlar, n0 < # wlar, m0 < m, avhdr0.sqn < avhdr.sqn, m < # wlar, m0 < # wlar, n0 < m, valid-peb(v0, n, mkpeb(aehdr0, avhdr0, buf0, m4, boolvar0)), valid-peb(v0, n, mkpeb(aehdr, avhdr, buf, m3, boolvar)), valid-peb(v0, m1, mkpeb(aechdr(m7), avhdr1, buf1, m5, false)), ∀ v, m. unique-elems(valid-sqns(v, m, apebs)) ⊦ avhdr1.sqn = (valid-sqns(v0, m1, apebs, m) ∪ (n = m1 ⊃ {avhdr.sqn} ;∅)).max, n0 = m, n0 = m0

Rule argument

fma: n = m1

Additional information

Used simplifier rules: ⊦ ∅ ∪ bag0 = bag0; (s)%union-ass: ⊦ bag ∪ bag3 ∪ bag4 = (bag ∪ bag3) ∪ bag4; from specification bag-union[nat-bag]%union-com: ⊦ bag ∪ bag2 = bag2 ∪ bag; from specification bag-union[nat-bag] Used formulas: n = m1