Apply H0 with
2f0a8...
Let x0 of type ((((ι → ο) → ο) → ο) → ο) → ((ι → ο) → ο) → ο be given.
Assume H1: ∀ x1 : (((ι → ο) → ο) → ο) → ο . ∀ x2 : ((ι → ο) → ο) → ο . x1 x2 ⟶ x1 (x0 x1).
Let x1 of type ο be given.
Assume H2: ∀ x2 : (((ι → ο) → ο) → ο) → (ι → ο) → ο . (∀ x3 : ((ι → ο) → ο) → ο . ∀ x4 : (ι → ο) → ο . x3 x4 ⟶ x3 (x2 x3)) ⟶ x1.
Apply H2 with
λ x2 : ((ι → ο) → ο) → ο . d94e6.. (x0 (a327b.. x2)).
Let x2 of type ((ι → ο) → ο) → ο be given.
Let x3 of type (ι → ο) → ο be given.
Assume H3: x2 x3.
Apply H1 with
a327b.. x2,
a4b00.. x3.
Apply unknownprop_184eb70be4d6de2c085355302621b5d7744ba1ec9b0a2c8c6f99ac8c0fb8596f with
x3,
x2.
The subproof is completed by applying H3.
Apply unknownprop_0dbccb569f5ddef423e0ee189c07cd3312d3f8e28ae0a046781df64b897d9254 with
x0 (a327b.. x2),
x2,
λ x4 : ((ι → ο) → ο) → ο . x2 (d94e6.. x4) leaving 2 subgoals.
The subproof is completed by applying L4.
Let x4 of type (ι → ο) → ο be given.
Assume H5: x2 x4.
Apply unknownprop_0d8f104370fcf0a65449637936f31a9241568316096de634f2dc46f7d76c2757 with
x4,
λ x5 x6 : (ι → ο) → ο . x2 x6.
The subproof is completed by applying H5.