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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιι be given.
Let x2 of type ιιο be given.
Let x3 of type ιιι be given.
Let x4 of type ι be given.
Assume H0: x4x0.
Let x5 of type ι be given.
Assume H1: x5x1 x4.
Assume H2: x2 x4 x5.
Apply UnionI with {{x3 x6 x7|x7 ∈ x1 x6,x2 x6 x7}|x6 ∈ x0}, x3 x4 x5, {x3 x4 x6|x6 ∈ x1 x4,x2 x4 x6} leaving 2 subgoals.
Apply ReplSepI with x1 x4, x2 x4, x3 x4, x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply ReplI with x0, λ x6 . {x3 x6 x7|x7 ∈ x1 x6,x2 x6 x7}, x4.
The subproof is completed by applying H0.