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Proofgold Proof

pf
Let x0 of type (CT2 (CT2 (ι → ι → ι))) → ι → ι → ι be given.
Assume H0: ∀ x1 : ((((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . 403c9.. x1 ⟶ fb516.. (x0 x1).
Apply unknownprop_b8b36d1309d23573d39f50bf215614db443fee92079ecdecdfe7e2612363510b with λ x1 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . e7e62.. (λ x2 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x0 (λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 x1 x2)).
Let x1 of type CT2 (ι → ι → ι) be given.
Assume H1: 64789.. x1.
Apply unknownprop_b8b36d1309d23573d39f50bf215614db443fee92079ecdecdfe7e2612363510b with λ x2 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x0 (λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 x1 x2).
Let x2 of type CT2 (ι → ι → ι) be given.
Assume H2: 64789.. x2.
Apply H0 with λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (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) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 x1 x2) = λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 x1 x2, 64789.. x1, 64789.. x2 leaving 3 subgoals.
Let x3 of type (CT2 (CT2 (ι → ι → ι))) → (CT2 (CT2 (ι → ι → ι))) → ο be given.
Assume H3: x3 (λ x4 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4 x1 x2) (λ x4 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (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.
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