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Proofgold Proof

pf
Let x0 of type ιο be given.
Let x1 of type ιιι be given.
Let x2 of type ιιι be given.
Assume H0: ∀ x3 x4 . x0 x3x0 x4x0 (x1 x3 x4).
Assume H1: ∀ x3 x4 x5 . x0 x3x0 x4x0 x5x2 x3 (x1 x4 x5) = x1 (x2 x3 x4) (x2 x3 x5).
Apply unknownprop_50a25df9f22e2243e87a46fa887321a360b2c9291209e6ac35742e8acd39bbae with x0, x1, λ x3 x4 . x2 x4 x3 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Assume H2: x0 x3.
Assume H3: x0 x4.
Assume H4: x0 x5.
Apply H1 with x5, x3, x4 leaving 3 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H2.
The subproof is completed by applying H3.