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Proof step 7 from proof bag-remadd-in (previous step)

∀ n. (bag0 -- n) ++ n = (n ∈ bag0 ⊃ bag0;bag0 ++ n) ⊦ bag0 -- n = bag0, m = n, n ∈ bag0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ n ∈ bag0 ↔ count(n, bag0) ≠ 0

Rule argument

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

Additional information

Used simplifier rules: ⊦ count(n, bag0) = 0 → bag0 -- n = bag0; (s) Used terms: bag0, n