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Proof step 4 from proof unique-elems-add (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ unique-elems(bag) ↔ (∀ n. count(n, bag) ≤ 1)
Proof step 6:
⊦ (∀ n. count(n, bag ++ m) ≤ 1) ↔ (∀ n. count(n, bag) ≤ 1) ∧ ¬ m ∈ bag

Rule argument

spec: <toplevel> name: unique-elems seq: ⊦ unique-elems(bag) ↔ (∀ n. count(n, bag) ≤ 1) subst: [bag] → [bag] flags: <all paths>

Additional information

Used terms: bag