Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Assume H0:
∀ x4 . In x4 x0 ⟶ ∀ x5 . In x5 (x1 x4) ⟶ x2 x4 x5 = x3 x4 x5.
Apply unknownprop_bd19dfd009a9cdfd7e00e5a28a77c1545e733688b5ba89bd8cc2f4f90ec5aaa3 with
λ x4 x5 : ι → (ι → ι) → (ι → ι → ι) → ι . x5 x0 x1 x2 = x5 x0 x1 x3.
Apply unknownprop_0642b50d39e38b4226ced44ea70045c3e9d51c2bcc4f9f4e004e3e32ae43373b with
x0,
λ x4 . lam (x1 x4) (λ x5 . x2 x4 x5),
λ x4 . lam (x1 x4) (λ x5 . x3 x4 x5).
Let x4 of type ι be given.
Apply unknownprop_0642b50d39e38b4226ced44ea70045c3e9d51c2bcc4f9f4e004e3e32ae43373b with
x1 x4,
λ x5 . x2 x4 x5,
λ x5 . x3 x4 x5.
Let x5 of type ι be given.
Assume H2:
In x5 (x1 x4).
Apply H0 with
x4,
x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.