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Proofgold Proof

pf
Let x0 of type (ιο) → ο be given.
Claim L0: ∃ x1 : (ι → ο) → ο . a4b00.. x1 = a4b00.. x0
Let x1 of type ο be given.
Assume H0: ∀ x2 : (ι → ο) → ο . a4b00.. x2 = a4b00.. x0x1.
Apply H0 with x0.
Let x2 of type (((ιο) → ο) → ο) → (((ιο) → ο) → ο) → ο be given.
Assume H1: x2 (a4b00.. x0) (a4b00.. x0).
The subproof is completed by applying H1.
Claim L1: ∀ x1 x2 : (ι → ο) → ο . a4b00.. x1 = a4b00.. x0a4b00.. x2 = a4b00.. x0x1 = x2
Let x1 of type (ιο) → ο be given.
Let x2 of type (ιο) → ο be given.
Assume H1: a4b00.. x1 = a4b00.. x0.
Assume H2: a4b00.. x2 = a4b00.. x0.
Apply unknownprop_0baf4c86bc102cc7ef5b5a6fba0fc5f1dad77a50acb8dbafd746ed7c6f61a4d8 with x2, x0, λ x3 x4 : (ι → ο) → ο . x1 = x4 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_0baf4c86bc102cc7ef5b5a6fba0fc5f1dad77a50acb8dbafd746ed7c6f61a4d8 with x1, x0.
The subproof is completed by applying H1.
Claim L2: a4b00.. (d94e6.. (a4b00.. x0)) = a4b00.. x0
Apply Descr_Vo2_prop with λ x1 : (ι → ο) → ο . a4b00.. x1 = a4b00.. x0 leaving 2 subgoals.
The subproof is completed by applying L0.
The subproof is completed by applying L1.
Apply unknownprop_0baf4c86bc102cc7ef5b5a6fba0fc5f1dad77a50acb8dbafd746ed7c6f61a4d8 with d94e6.. (a4b00.. x0), x0.
The subproof is completed by applying L2.