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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: 68498.. x0 x1.
Assume H3: 68498.. x0 x2.
Assume H4: SNo x3.
Assume H5: SNo x4.
Assume H6: binunion x1 {(λ x6 . SetAdjoin x6 (Sing x0)) x5|x5 ∈ x3} = binunion x2 {(λ x6 . SetAdjoin x6 (Sing x0)) x5|x5 ∈ x4}.
Apply set_ext with x3, x4 leaving 2 subgoals.
Apply unknownprop_a97133940ac2c1ce9f083f5e9e39454f8b1e260e2b08e635a6abc9c31862ea27 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_a97133940ac2c1ce9f083f5e9e39454f8b1e260e2b08e635a6abc9c31862ea27 with x0, x2, x1, x4, x3 leaving 6 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H5.
The subproof is completed by applying H4.
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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