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Proofgold Proof

pf
Let x0 of type ιι be given.
Let x1 of type ιιο be given.
Assume H0: ∀ x2 x3 . x1 x3 x2x1 x3 (x0 x2).
Let x2 of type ι be given.
Let x3 of type ι be given.
Assume H1: x1 x3 x2.
Apply unknownprop_8f091fac19628539fcf2e218e3dc2a99ae1149b00810a44df3df9898ec6617fb with x0, x1, ChurchNum_ii_4 ChurchNum2 x0 x2, x3 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply unknownprop_8f091fac19628539fcf2e218e3dc2a99ae1149b00810a44df3df9898ec6617fb with x0, x1, x2, x3 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.