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Proof step 6 from proof unique-elems-add (previous step)

⊦ (∀ n. count(n, bag ++ m) ≤ 1) ↔ (∀ n. count(n, bag) ≤ 1) ∧ ¬ m ∈ bag

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ n ∈ bag0 ↔ count(n, bag0) ≠ 0
Proof step 8:
⊦ (∀ n. count(n, bag ++ m) ≤ 1) ↔ (∀ n. count(n, bag) ≤ 1) ∧ ¬ count(m, bag) ≠ 0

Rule argument

spec: bag-union, inst: nat-bag name: in seq: ⊦ n ∈ bag0 ↔ count(n, bag0) ≠ 0 subst: [bag0, n] → [bag, m] flags: <all paths>

Additional information

Used terms: bag, m