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Proof step 12 from proof in-01-01 (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 13:
a ∈ x0, a ∈ y, ∀ a, y. a ∈ y → (a ∈ filter(x0, y) ↔ a ∈ x0) ⊦ a ∈ filter(x0, y) ↔ a ∈ x0, a0 ∈ y
Proof step 15:
a ∈ y, ∀ a, y. a ∈ y → (a ∈ filter(x0, y) ↔ a ∈ x0) ⊦ a ∈ x0, a ∈ filter(x0, y) ↔ a ∈ x0, a0 ∈ y

Rule argument

fma: a ∈ x0

Additional information

Used formulas: a ∈ x0