Proofgold Proof

pf

Let x0 of type ι be given.

Let x1 of type ι be given.

Let x2 of type ι be given.

Assume H0: nIn x2 (binunion x0 x1).

Apply andI with nIn x2 x0, nIn x2 x1 leaving 2 subgoals.

Assume H1: x2 ∈ x0.

Apply H0.

Apply binunionI1 with x0, x1, x2.

The subproof is completed by applying H1.

Assume H1: x2 ∈ x1.

Apply H0.

Apply binunionI2 with x0, x1, x2.

The subproof is completed by applying H1.

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