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Proof step 3 from proof in-05 (previous step)

a ∈ x, a ∈ filter(x, y) ⊦ a ∈ y

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ a ∈ filter(x, y) ↔ a ∈ x ∧ a ∈ y

Rule argument

spec: <toplevel> name: filt-in seq: ⊦ a ∈ filter(x, y) ↔ a ∈ x ∧ a ∈ y subst: [y, x, a] → [y, x, a] flags: <all paths>

Additional information

Used terms: y, x, a