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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Apply unknownprop_99075cb60dd6ee1ecde84daf9e64c3f2c524bf0d235a5b34e6bf4c80b29f7ce1 with x0, x1, x2, x3, 0, λ x4 x5 . x5 = f4b0e.. x0 x1 x2 x3.
Apply Repl_Empty with λ x4 . SetAdjoin x4 (Sing 5), λ x4 x5 . binunion (f4b0e.. x0 x1 x2 x3) x5 = f4b0e.. x0 x1 x2 x3.
Apply binunion_idr with f4b0e.. x0 x1 x2 x3, λ x4 x5 . x5 = f4b0e.. x0 x1 x2 x3.
Let x4 of type ιιο be given.
Assume H0: x4 (f4b0e.. x0 x1 x2 x3) (f4b0e.. x0 x1 x2 x3).
The subproof is completed by applying H0.