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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: nat_p x0.
Assume H1: 1 ∈ x0.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Assume H2: SNo x1.
Assume H3: SNo x2.
Assume H4: SNo x3.
Assume H5: SNo x4.
Assume H6: e9c39.. x0 x1 x2 = e9c39.. x0 x3 x4.
Apply set_ext with x2, x4 leaving 2 subgoals.
Apply unknownprop_78da5370b3190c65447d48ceafc97cfa2d590a8a3a8a14af4f82f908ac321b60 with x0, x1, x2, x3, x4 leaving 6 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
Apply unknownprop_78da5370b3190c65447d48ceafc97cfa2d590a8a3a8a14af4f82f908ac321b60 with x0, x3, x4, x1, x2 leaving 6 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H5.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H6 with λ x6 x7 . x5 x7 x6.
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