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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: 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 x1, x2 leaving 2 subgoals.
Apply unknownprop_93892cbce277566e8cc1efdde5180cb4698c4865b713b4e41b7f3e1218e2f0cf with x0, x1, x2, x3, x4 leaving 4 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 H4.
Apply unknownprop_93892cbce277566e8cc1efdde5180cb4698c4865b713b4e41b7f3e1218e2f0cf with x0, x2, x1, x4, x3 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H3.
Let x5 of type ι → ι → ο be given.
The subproof is completed by applying H4 with λ x6 x7 . x5 x7 x6.
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