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Proof step 20 from proof unique-sqns-write-valid (previous step)

apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), m < # apebs, valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), ∀ v, m. unique-elems(valid-sqns(v, m, apebs)) ⊦ unique-elems(valid-sqns(v, m2, apebs) ∪ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {avhdr.sqn} ;∅)), v = avhdr.vol ∧ m2 = avhdr.leb

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Proof step 21:
apebs[m] = mkpeb(aehdr, avhdr, buf0, m0, boolvar0), m < # apebs, valid-peb(mkpeb(aehdr, avhdr, buf0, m0, boolvar0)), valid-peb(mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), ∀ v, m. unique-elems(valid-sqns(v, m, apebs)) ⊦ unique-elems(valid-sqns(v, m2, apebs) ∪ (valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)) ⊃ {avhdr.sqn} ;∅)), valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1)), v = avhdr.vol ∧ m2 = avhdr.leb

Rule argument

fma: valid-peb(v, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1))

Additional information

Used simplifier rules: ⊦ valid-peb(v0, m0, apeb) → (valid-peb(v1, m1, apeb) ↔ v0 = v1 ∧ m0 = m1); (s)% ⊦ bag ∪ {n} = bag ++ n; (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]% ⊦ unique-elems(bag ++ m) ↔ unique-elems(bag) ∧ ¬ m ∈ bag; (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, m2, mkpeb(aehdr, avhdr, buf1, m1, boolvar1))