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Proof step 31 from proof valid-wl-write-valid (previous step)

# apebs = # wlar, avhdr0.sqn = (valid-sqns(v, m5, apebs) ∪ (valid-peb(v, m5, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {avhdr.sqn} ;∅)).max, apebs[n] = mkpeb(aechdr(m4), avhdr0, buf, m3, false), wlar[m] = wl-entry(m2, used), apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), wlar[n] = wl-entry(m4, used), n < # wlar, m < # wlar, valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), valid-peb(v, m5, mkpeb(aechdr(m4), avhdr0, buf, m3, false)) ⊦ avhdr0.sqn = valid-sqns(v, m5, apebs).max, n = m, v = avhdr.vol ∧ m5 = avhdr.leb

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: valid-peb(v, m5, mkpeb(aehdr, avhdr, buf1, m1, boolvar1))

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]%⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ bag ∪ {n} = bag ++ n; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.vol = v; (s)%⊦ valid-peb(v, m, mkpeb(aehdr, avhdr, buf, m0, boolvar)) → avhdr.leb = m; (s) Used formulas: valid-peb(v, m5, mkpeb(aehdr, avhdr, buf1, m1, boolvar1))