Let x0 of type ι → ο be given.

Claim L0: ∃ x1 : ι → ο . 407b5.. x1 = 407b5.. x0

Let x1 of type ο be given.

Assume H0: ∀ x2 : ι → ο . 407b5.. x2 = 407b5.. x0 ⟶ x1.

Apply H0 with x0.

Let x2 of type ((ι → ο) → ο) → ((ι → ο) → ο) → ο be given.

Assume H1: x2 (407b5.. x0) (407b5.. x0).

The subproof is completed by applying H1.

Claim L1: ∀ x1 x2 : ι → ο . 407b5.. x1 = 407b5.. x0 ⟶ 407b5.. x2 = 407b5.. x0 ⟶ x1 = x2

Let x1 of type ι → ο be given.

Let x2 of type ι → ο be given.

Assume H1: 407b5.. x1 = 407b5.. x0.

Assume H2: 407b5.. x2 = 407b5.. x0.

Apply unknownprop_f6212d6ba4366f14f16f0857e6566c26f7bd27125deb5e4c2748921fd5fa9530 with x2, x0, λ x3 x4 : ι → ο . x1 = x4 leaving 2 subgoals.

The subproof is completed by applying H2.

Apply unknownprop_f6212d6ba4366f14f16f0857e6566c26f7bd27125deb5e4c2748921fd5fa9530 with x1, x0.

The subproof is completed by applying H1.

Apply Descr_Vo1_prop with λ x1 : ι → ο . 407b5.. x1 = 407b5.. x0 leaving 2 subgoals.

The subproof is completed by applying L0.

The subproof is completed by applying L1.

Apply unknownprop_f6212d6ba4366f14f16f0857e6566c26f7bd27125deb5e4c2748921fd5fa9530 with 3e5e9.. (407b5.. x0), x0.

The subproof is completed by applying L2.

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Proofgold Proof