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Proof step 3 from proof notin-02 (previous step)

∀ a, y. a ∈ filter(x0, y) → a ∈ y, a ∈ filter(a0 + x0, y) ⊦ a ∈ y

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
a ∈ filter(a0 ' + x0, y), ∀ a, y. a ∈ filter(x0, y) → a ∈ y ⊦ a ∈ y

Rule argument

Additional information

Used simplifier rules: c: ⊦ a + x = a ' + x; from specification list