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Proof step 5 from proof notin-01 (previous step)

a ∈ y, a ∈ (a0 ' + x0) \ y, ∀ a1, y0. ¬ a1 ∈ y0 ∨ ¬ a1 ∈ x0 \ y0 ⊦

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 6:
a ∈ (a0 ' + x0) \ y, a ∈ y, a0 ∈ y, ∀ a1, y0. ¬ a1 ∈ y0 ∨ ¬ a1 ∈ x0 \ y0 ⊦
Proof step 8:
a ∈ (a0 ' + x0) \ y, a ∈ y, ∀ a1, y0. ¬ a1 ∈ y0 ∨ ¬ a1 ∈ x0 \ y0 ⊦ a0 ∈ y

Rule argument

fma: a0 ∈ y

Additional information

Used formulas: a0 ∈ y