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Proof step 3 from proof sum-of-differences-in (previous step)

sum-of-differences(n, bag) < n - m, m ∈ bag ⊦

User applied rule structural induction

And obtained the following new goals

Proof step 4:
sum-of-differences(n, bag0 ++ vtblpnum) < n - m, m ∈ bag0 ++ vtblpnum, ∀ n, m. ¬(sum-of-differences(n, bag0) < n - m ∧ m ∈ bag0) ⊦

Rule argument

indvar: bag

Additional information

Used simplifier rules: nat-bag generated by ∅, ++;;% ⊦ ¬ n ∈ ∅; (s)