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Proof step 4 from proof unique-elems-rem-notin (previous step)

unique-elems(bag), m ∈ bag -- n ⊦ m ≠ n ∧ m ∈ bag

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ n ∈ bag0 ↔ count(n, bag0) ≠ 0
Proof step 6:
unique-elems(bag) ⊦ count(m, bag -- n) = 0, m ≠ n ∧ m ∈ bag

Rule argument

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

Additional information

Used terms: bag -- n, m