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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.
Assume H0: prim1 x2 (0ac37.. (94f9e.. x0 (λ x3 . f6917.. x3)) (94f9e.. x1 (λ x3 . 09364.. x3))).
Apply unknownprop_b46721c187c37140cbae22d356b00ba89f4126d81d8665e4be15b5a58c78d06f with 94f9e.. x0 (λ x3 . f6917.. x3), 94f9e.. x1 (λ x3 . 09364.. x3), x2, or (∃ x3 . and (prim1 x3 x0) (x2 = f6917.. x3)) (∃ x3 . and (prim1 x3 x1) (x2 = 09364.. x3)) leaving 3 subgoals.
The subproof is completed by applying H0.
Assume H1: prim1 x2 (94f9e.. x0 (λ x3 . f6917.. x3)).
Apply orIL with ∃ x3 . and (prim1 x3 x0) (x2 = f6917.. x3), ∃ x3 . and (prim1 x3 x1) (x2 = 09364.. x3).
Apply unknownprop_04b90adbc2ec31bffcbccbbe8e8bda04aa9f95ec157434af0f1f260c2db4f24e with x0, f6917.., x2.
The subproof is completed by applying H1.
Assume H1: prim1 x2 (94f9e.. x1 (λ x3 . 09364.. x3)).
Apply orIR with ∃ x3 . and (prim1 x3 x0) (x2 = f6917.. x3), ∃ x3 . and (prim1 x3 x1) (x2 = 09364.. x3).
Apply unknownprop_04b90adbc2ec31bffcbccbbe8e8bda04aa9f95ec157434af0f1f260c2db4f24e with x1, 09364.., x2.
The subproof is completed by applying H1.