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Proof step 20 from proof unique-elems-add (previous step)

count(m, bag) = 0, ∀ n. count(n, bag) ≤ 1 ⊦ (n = m ⊃ 1;0) + count(n, bag) = 1, (n = m ⊃ 1;0) + count(n, bag) = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
count(m, bag) = 0, ∀ n. count(n, bag) ≤ 1 ⊦ count(n, bag) = 1, count(n, bag) = 0

Rule argument

Additional information

Used simplifier rules: ⊦ n + 0 = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = 1 ↔ m = 0 ∧ n = 1 ∨ n = 0 ∧ m = 1; (ws)