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Proof step 12 from proof f-rm (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ a ∈ filter(x, y) ↔ a ∈ x ∧ a ∈ y
Proof step 14:
a ∈ x0 ∧ a ∈ y, a ∈ y, ∀ y. filter(rmdup(x0), y) = rmdup(filter(x0, y)) ⊦ filter(rmdup(a ' + x0), y) = rmdup(filter(x0, 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