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Proof step 10 from proof unique-elems-rem-notin (previous step)

unique-elems(bag) ⊦ count(m, bag) - (m = n ∧ count(n, bag) ≠ 0 ⊃ 1;0) = 0, m ≠ n ∧ m ∈ bag

Heuristic if-then-else split applied rule case distinction

And obtained the following new goals

Proof step 11:
m = n, unique-elems(bag) ⊦ count(m, bag) - 1 = 0, count(n, bag) = 0, m ≠ n ∧ m ∈ bag
Proof step 17:
unique-elems(bag), m ≠ n ∨ count(n, bag) = 0 ⊦ count(m, bag) - 0 = 0, m ≠ n ∧ m ∈ bag

Rule argument

pos: right 1

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