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Proof step 7 from proof sum-of-differences-in (previous step)

(n - vtblpnum) + sum-of-differences(n, bag0) < n - m, ∀ n0, m0. ¬ sum-of-differences(n0, bag0) < n0 - m0 ∨ ¬ m0 ∈ bag0, m ∈ bag0 ∨ m = vtblpnum ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
(n - vtblpnum) + sum-of-differences(n, bag0) < n - m, m ∈ bag0, ∀ n0, m0. ¬ sum-of-differences(n0, bag0) < n0 - m0 ∨ ¬ m0 ∈ bag0 ⊦ m = vtblpnum

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ m + n < m; (s)