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Proof step 7 from proof bag-rm-add-eq (previous step)

(count(a, bag) - 1) + 1 = count(a, bag) ⊦ count(a, bag) = 0, a ∈ bag

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
⊦ count(a, bag) = 0, a ∈ bag

Rule argument

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)