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Proof step 1 from proof ext-rec (conclusion)

⊦ bag1 = bag0 ++ a ↔ (∀ b. count(b, bag1) = (a = b ⊃ 1;0) + count(b, bag0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
∀ b. count(b, bag1) = (a = b ⊃ 1;0) + count(b, bag0) ⊦ bag1 = bag0 ++ a

Rule argument

Additional information

Used simplifier rules: count-insert: ⊦ count(a, bag ++ b) = (a = b ⊃ 1;0) + count(a, bag);%c: ⊦ m + n = n + m; from specification nat-basic2%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic2%eq-01: ⊦ m + n = m + n0 ↔ n = n0; from specification nat-basic2