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Proof step 8 from proof notin-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
a ∈ y, a ∈ x0 \ y, ∀ a1, y0. ¬ a1 ∈ y0 ∨ ¬ a1 ∈ x0 \ y0 ⊦ a0 ∈ y

Rule argument

Additional information

Used simplifier rules: diff-n: ⊦ ¬ a ∈ y → (a ' + x) \ y = a + (x \ y);% ⊦ a ∈ b ' ↔ a = b; (s)% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a + x = a ' + x; (s)