Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_da1ac74e7171cfbc42378617a62cb62f2a4d8bf3a5c1e029c4b4e4f12cda8627 with
x0,
λ x2 x3 . prim1 x1 x3 ⟶ or (x1 = 4a7ef..) (∃ x4 . and (prim1 x4 x0) (x1 = 09364.. x4)).
Apply unknownprop_b46721c187c37140cbae22d356b00ba89f4126d81d8665e4be15b5a58c78d06f with
91630.. 4a7ef..,
94f9e.. x0 (λ x2 . 09364.. x2),
x1,
or (x1 = 4a7ef..) (∃ x2 . and (prim1 x2 x0) (x1 = 09364.. x2)) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply orIL with
x1 = 4a7ef..,
∃ x2 . and (prim1 x2 x0) (x1 = 09364.. x2).
Apply unknownprop_30833a9978e304b25ffd59c347245315985872140acc9e441a97543a28184d79 with
4a7ef..,
x1.
The subproof is completed by applying H1.
Apply orIR with
x1 = 4a7ef..,
∃ x2 . and (prim1 x2 x0) (x1 = 09364.. x2).
Apply unknownprop_04b90adbc2ec31bffcbccbbe8e8bda04aa9f95ec157434af0f1f260c2db4f24e with
x0,
09364..,
x1.
The subproof is completed by applying H1.