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Proofgold Proof

pf
Let x0 of type ι(ι((ιο) → ο) → ο) → ((ιο) → ο) → ο be given.
Assume H0: ∀ x1 . ∀ x2 x3 : ι → ((ι → ο) → ο) → ο . (∀ x4 . In x4 x1x2 x4 = x3 x4)x0 x1 x2 = x0 x1 x3.
Apply unknownprop_acac0f89c78f08b97a9fe27ba4af5f929f74e43a9a77a0beb38d70975279c8b8 with λ x1 . 31b02.. x0 x1 (2bbaf.. x0 x1).
Let x1 of type ι be given.
Assume H1: ∀ x2 . In x2 x131b02.. x0 x2 (2bbaf.. x0 x2).
Apply Descr_Vo3_prop with 31b02.. x0 x1 leaving 2 subgoals.
Let x2 of type ο be given.
Assume H2: ∀ x3 : ((ι → ο) → ο) → ο . 31b02.. x0 x1 x3x2.
Apply H2 with x0 x1 (2bbaf.. x0).
Apply unknownprop_200877d319f2b36e0d8a103c6387513d7834e47d124e1c76044220c6adec8488 with x0, x1, 2bbaf.. x0.
The subproof is completed by applying H1.
Apply unknownprop_f8e298c212ecb25f425f9e64ca55910b86e06fb1674aefb60326d44f370d161e with x0, x1.
The subproof is completed by applying H0.