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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0u6.
Let x1 of type ι be given.
Assume H1: x1u6.
Assume H2: In2_lexicographic x0 u2 x1 u1.
Apply H2 with False leaving 2 subgoals.
Assume H3: u2u1.
Apply In_no2cycle with u1, u2 leaving 2 subgoals.
The subproof is completed by applying In_1_2.
The subproof is completed by applying H3.
Assume H3: and (u2 = u1) (x0x1).
Apply H3 with False.
Assume H4: u2 = u1.
Apply FalseE with x0x1False.
Apply In_irref with u1.
Apply H4 with λ x2 x3 . u1x2.
The subproof is completed by applying In_1_2.