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Proof step 3 from proof toSet-app (previous step)

⊦ ∀ a. a ∈ (x0 + x1).toSet ↔ a ∈ x0.toSet ∪ x1.toSet

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ a ∈ x.toSet ↔ a ∈ x
Proof step 5:
⊦ a ∈ x0 ∨ a ∈ x1 ↔ a ∈ x0.toSet ∪ x1.toSet

Rule argument

Additional information

Used simplifier rules: toSet-ext: ⊦ a ∈ x.toSet ↔ a ∈ x;%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ a ∈ x + y ↔ a ∈ x ∨ a ∈ y; (s)