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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ιο be given.
Let x2 of type ι be given.
Assume H0: nIn x2 (Sep x0 (λ x3 . x1 x3)).
Assume H1: nIn x2 x0False.
Assume H2: not (x1 x2)False.
Apply unknownprop_8369708f37c0d20e10b6156293f1b207e835dfc563ff7fbfa059bf26c84ddb80 with x2, Sep x0 (λ x3 . x1 x3) leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_646b3add51cf8f8e84959b456822a93c7e59b2f394a14897b6752b9d28c1a75d with x0, x1, x2 leaving 2 subgoals.
Apply unknownprop_75b5762e65badae8f9531d40fddd332ff95b59f608d93c7a55f19f4fa5ef37d5 with x2, x0.
The subproof is completed by applying H1.
Apply unknownprop_b777a79c17f16cd28153af063df26a4626b11c1f1d4394d7f537c11837ab0962 with x1 x2.
The subproof is completed by applying H2.