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Proof step 3 from proof still-in-rem (previous step)

a ∈ bag0 -- b ⊦ a ∈ bag0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ a ∈ bag ↔ count(a, bag) ≠ 0
Proof step 5:
⊦ count(a, bag0 -- b) = 0, a ∈ bag0

Rule argument

spec: <toplevel> name: in seq: ⊦ a ∈ bag ↔ count(a, bag) ≠ 0 subst: [bag, a] → [bag0 -- b, a] flags: <all paths>

Additional information

Used terms: bag0 -- b, a