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 → ο be given.
Assume H1:
∀ x4 . In x4 x0 ⟶ x3 (Inj0 x4).
Assume H2:
∀ x4 . In x4 x1 ⟶ x3 (Inj1 x4).
Apply unknownprop_eb8e8f72a91f1b934993d4cb19c84c8270f73a3626f3022b683d960a7fef89cb with
∃ x4 . and (In x4 x0) (x2 = Inj0 x4),
∃ x4 . and (In x4 x1) (x2 = Inj1 x4),
x3 x2 leaving 3 subgoals.
Apply unknownprop_7d032697ca40cddbc051c2380c77c6793240c9afe41b60a5fed4aabdd07b91ac with
x0,
x1,
x2.
The subproof is completed by applying H0.
Assume H3:
∃ x4 . and (In x4 x0) (x2 = Inj0 x4).
Apply unknownprop_3848cfb1fd522cb609408da39f227a9c05924a24919f21041d0880590b824ef5 with
λ x4 . In x4 x0,
λ x4 . x2 = Inj0 x4,
x3 x2 leaving 2 subgoals.
The subproof is completed by applying H3.
Let x4 of type ι be given.
Apply H5 with
λ x5 x6 . x3 x6.
Apply H1 with
x4.
The subproof is completed by applying H4.
Assume H3:
∃ x4 . and (In x4 x1) (x2 = Inj1 x4).
Apply unknownprop_3848cfb1fd522cb609408da39f227a9c05924a24919f21041d0880590b824ef5 with
λ x4 . In x4 x1,
λ x4 . x2 = Inj1 x4,
x3 x2 leaving 2 subgoals.
The subproof is completed by applying H3.
Let x4 of type ι be given.
Apply H5 with
λ x5 x6 . x3 x6.
Apply H2 with
x4.
The subproof is completed by applying H4.