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Proof step 8 from proof f-rm (previous step)

a ∈ y, ∀ y. filter(rmdup(x0), y) = rmdup(filter(x0, y)) ⊦ filter(rmdup(a ' + x0), y) = a ' + rmdup(filter(x0, y)), a ∈ filter(x0, y)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ a ∈ filter(x, y) ↔ a ∈ x ∧ a ∈ y
Proof step 10:
a ∈ y, ∀ y. filter(rmdup(x0), y) = rmdup(filter(x0, y)) ⊦ filter(rmdup(a ' + x0), y) = a ' + rmdup(filter(x0, y)), a ∈ x0 ∧ a ∈ y

Rule argument

spec: list-set inst: name: filt-in seq: ⊦ a ∈ filter(x, y) ↔ a ∈ x ∧ a ∈ y subst: [y, x, a] → [y, x0, a] flags: rewrite, current

Additional information

Used terms: y, x0, a