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Proofgold Proof

pf
Let x0 of type ι → ι → ι be given.
Let x1 of type ι → ι → ι be given.
Assume H0: fb516.. x0.
Assume H1: fb516.. x1.
Apply H0 with fb516.. (cc64c.. x0 x1) leaving 2 subgoals.
Assume H2: x0 = ChurchBoolTru.
Apply H2 with λ x2 x3 : ι → ι → ι . fb516.. (cc64c.. x3 x1).
The subproof is completed by applying unknownprop_4b2c4a0487c2b1a228c5d07bbf352ffca25633bec988b0f94ee850e02347e107.
Assume H2: x0 = ChurchBoolFal.
Apply H2 with λ x2 x3 : ι → ι → ι . fb516.. (cc64c.. x3 x1).
Apply unknownprop_fe36caae5784dcaccf90e3c33c4c3db05a48fc46bf7e1321a13b032e9121e798 with λ x2 x3 : ι → ι → ι . fb516.. (cc64c.. x3 x1).
The subproof is completed by applying H1.
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