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Proof step 17 from proof unique-elems-add (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
count(m, bag) = 0, ∀ n. count(n, bag) ≤ 1 ⊦ count(n, bag ++ m) = 0, count(n, bag ++ m) = 1

Rule argument

Additional information

Used simplifier rules: ⊦ 1 < m ↔ ¬(m = 0 ∨ m = 1); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)