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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0u6.
Assume H1: In2_lexicographic u2 x0 u1 x0.
Apply H1 with False leaving 2 subgoals.
Assume H2: x0x0.
Apply In_irref with x0.
The subproof is completed by applying H2.
Assume H2: and (x0 = x0) (u2u1).
Apply H2 with False.
Assume H3: x0 = x0.
Assume H4: 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 H4.