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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ιι be given.
Let x3 of type ιι be given.
Let x4 of type ιο be given.
Assume H0: ∀ x5 . x5x0x4 (x2 x5).
Assume H1: ∀ x5 . x5x1x4 (x3 x5).
Let x5 of type ι be given.
Apply binunionE' with {x2 x6|x6 ∈ x0}, {x3 x6|x6 ∈ x1}, x5, x4 x5 leaving 2 subgoals.
Apply ReplE' with x0, x2, x4, x5.
The subproof is completed by applying H0.
Apply ReplE' with x1, x3, x4, x5.
The subproof is completed by applying H1.