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Proof step 4 from proof notin-02 (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 5:
a0 ∈ y, a ∈ filter(a0 ' + x0, y), ∀ a, y. a ∈ filter(x0, y) → a ∈ y ⊦ a ∈ y
Proof step 7:
a ∈ filter(a0 ' + x0, y), ∀ a, y. a ∈ filter(x0, y) → a ∈ y ⊦ a0 ∈ y, a ∈ y

Rule argument

fma: a0 ∈ y

Additional information

Used formulas: a0 ∈ y