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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 ι be given.
Apply unknownprop_5d43e074a46031aba9b972e1346a32eab5bc6d7f8cd872222d3a15fe3889dd90 with λ x3 x4 : ι → ι → ο . x4 x2 x0x4 x2 x1x4 x2 (binintersect x0 x1).
Assume H0: ∀ x3 . In x3 x2In x3 x0.
Assume H1: ∀ x3 . In x3 x2In x3 x1.
Let x3 of type ι be given.
Assume H2: In x3 x2.
Apply unknownprop_7e73699eda4c2a35af8db1aea1ddace7d2346405cd3944ace259823e1ec33cf3 with x0, x1, x3 leaving 2 subgoals.
Apply H0 with x3.
The subproof is completed by applying H2.
Apply H1 with x3.
The subproof is completed by applying H2.