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Proofgold Proof

pf
Let x0 of type ((ιο) → ο) → ο be given.
Claim L0: ∃ x1 : ((ι → ο) → ο) → ο . a327b.. x1 = a327b.. x0
Let x1 of type ο be given.
Assume H0: ∀ x2 : ((ι → ο) → ο) → ο . a327b.. x2 = a327b.. x0x1.
Apply H0 with x0.
Let x2 of type ((((ιο) → ο) → ο) → ο) → ((((ιο) → ο) → ο) → ο) → ο be given.
Assume H1: x2 (a327b.. x0) (a327b.. x0).
The subproof is completed by applying H1.
Claim L1: ∀ x1 x2 : ((ι → ο) → ο) → ο . a327b.. x1 = a327b.. x0a327b.. x2 = a327b.. x0x1 = x2
Let x1 of type ((ιο) → ο) → ο be given.
Let x2 of type ((ιο) → ο) → ο be given.
Assume H1: a327b.. x1 = a327b.. x0.
Assume H2: a327b.. x2 = a327b.. x0.
Apply unknownprop_fb936e779a336113a4fb7f3c7b779c1e8f8958132dfedde97188f6d659f336c8 with x2, x0, λ x3 x4 : ((ι → ο) → ο) → ο . x1 = x4 leaving 2 subgoals.
The subproof is completed by applying H2.
Apply unknownprop_fb936e779a336113a4fb7f3c7b779c1e8f8958132dfedde97188f6d659f336c8 with x1, x0.
The subproof is completed by applying H1.
Claim L2: a327b.. (dba53.. (a327b.. x0)) = a327b.. x0
Apply Descr_Vo3_prop with λ x1 : ((ι → ο) → ο) → ο . a327b.. x1 = a327b.. x0 leaving 2 subgoals.
The subproof is completed by applying L0.
The subproof is completed by applying L1.
Apply unknownprop_fb936e779a336113a4fb7f3c7b779c1e8f8958132dfedde97188f6d659f336c8 with dba53.. (a327b.. x0), x0.
The subproof is completed by applying L2.