Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
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.
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.
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.