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Proofgold Proof

pf
Let x0 of type ι(ιιο) → ιο be given.
Assume H0: ∀ x1 . ∀ x2 x3 : ι → ι → ο . (∀ x4 . In x4 x1x2 x4 = x3 x4)x0 x1 x2 = x0 x1 x3.
Let x1 of type ι be given.
Let x2 of type ι(ιο) → ο be given.
Assume H1: ∀ x3 . ∀ x4 : ι → ι → ο . (∀ x5 . In x5 x3x2 x5 (x4 x5))x2 x3 (x0 x3 x4).
Apply H1 with x1, f9c5e.. x0.
Let x3 of type ι be given.
Assume H2: In x3 x1.
Apply unknownprop_33d3425701b53c0a6330607b14fbeb2cf0a994c3f62ac0cf25e89ab42e5460f2 with x0, x3, x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.