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Proofgold Proof

pf
Let x0 of type ο be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Assume H0: x0.
Apply If_i_correct with x0, x1, x2, If_i x0 x1 x2 = x1 leaving 2 subgoals.
Assume H1: and x0 (If_i x0 x1 x2 = x1).
Apply andER with x0, If_i x0 x1 x2 = x1.
The subproof is completed by applying H1.
Assume H1: and (not x0) (If_i x0 x1 x2 = x2).
Apply andEL with not x0, If_i x0 x1 x2 = x2, If_i x0 x1 x2 = x1 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.