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Proof step 7 from proof union (previous step)

a ≠ a0, ∀ a, bag1. count(a, bag ∪ bag1) = count(a, bag) + count(a, bag1) ⊦ count(a, bag ∪ bag1) = count(a, bag ++ a0) + count(a, bag1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
∀ a, bag1. count(a, bag ∪ bag1) = count(a, bag) + count(a, bag1) ⊦ a = a0, count(a, bag ∪ bag1) = count(a, bag) + count(a, bag1)

Rule argument

Additional information

Used simplifier rules: count-other: ⊦ a ≠ b → count(a, bag ++ b) = count(a, bag); from specification bag-basic