Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply unknownprop_fc3f08095f77ec388b89b48e2b52040a80a894c58ae8421f993dbbc015fb91c5 with
λ x3 x4 : ι → ι → ι . In x2 (x4 x0 x1) ⟶ ∀ x5 : ι → ο . (∀ x6 . In x6 x0 ⟶ x5 (Inj0 x6)) ⟶ (∀ x6 . Subq x6 x1 ⟶ x5 (Inj1 x6)) ⟶ x5 x2.
Let x3 of type ι → ο be given.
Assume H1:
∀ x4 . In x4 x0 ⟶ x3 (Inj0 x4).
Assume H2:
∀ x4 . Subq x4 x1 ⟶ x3 (Inj1 x4).
Apply unknownprop_18583690a94a3aabb1b201c712283c6f832bd4e90b0730d0c8623d2e4a7a992a with
x0,
Power x1,
x2,
λ x4 . x3 x4 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Let x4 of type ι be given.
Apply H2 with
x4.
Apply unknownprop_b8811722bb772bba243207d8ee471ba24f8b88e821f7737307414168e638d2c6 with
x1,
x4.
The subproof is completed by applying H3.