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Proofgold Proof

pf
Let x0 of type (CT2 (ιιι)) → ιιι be given.
Assume H0: ∀ x1 : ((ι → ι → ι)(ι → ι → ι)ι → ι → ι)ι → ι → ι . 64789.. x1fb516.. (x0 x1).
Apply unknownprop_b68b358a15caf16d5fad4af9ff92c73636fdab478a3b1e7982a0f7f63be43fee with λ x1 : ι → ι → ι . 0f571.. (λ x2 : ι → ι → ι . x0 (λ x3 : (ι → ι → ι)(ι → ι → ι)ι → ι → ι . x3 x1 x2)).
Let x1 of type ιιι be given.
Assume H1: fb516.. x1.
Apply unknownprop_b68b358a15caf16d5fad4af9ff92c73636fdab478a3b1e7982a0f7f63be43fee with λ x2 : ι → ι → ι . x0 (λ x3 : (ι → ι → ι)(ι → ι → ι)ι → ι → ι . x3 x1 x2).
Let x2 of type ιιι be given.
Assume H2: fb516.. x2.
Apply H0 with λ x3 : (ι → ι → ι)(ι → ι → ι)ι → ι → ι . x3 x1 x2.
Apply and3I with (λ x3 : (ι → ι → ι)(ι → ι → ι)ι → ι → ι . x3 x1 x2) = λ x3 : (ι → ι → ι)(ι → ι → ι)ι → ι → ι . x3 x1 x2, fb516.. x1, fb516.. x2 leaving 3 subgoals.
Let x3 of type (CT2 (ιιι)) → (CT2 (ιιι)) → ο be given.
Assume H3: x3 (λ x4 : (ι → ι → ι)(ι → ι → ι)ι → ι → ι . x4 x1 x2) (λ x4 : (ι → ι → ι)(ι → ι → ι)ι → ι → ι . x4 x1 x2).
The subproof is completed by applying H3.
The subproof is completed by applying H1.
The subproof is completed by applying H2.