Apply H0 with
fb56c...
Let x0 of type (((ι → ο) → ο) → ο) → (ι → ο) → ο be given.
Assume H1: ∀ x1 : ((ι → ο) → ο) → ο . ∀ x2 : (ι → ο) → ο . x1 x2 ⟶ x1 (x0 x1).
Let x1 of type ο be given.
Assume H2: ∀ x2 : ((ι → ο) → ο) → ι → ο . (∀ x3 : (ι → ο) → ο . ∀ x4 : ι → ο . x3 x4 ⟶ x3 (x2 x3)) ⟶ x1.
Apply H2 with
λ x2 : (ι → ο) → ο . 3e5e9.. (x0 (a4b00.. x2)).
Let x2 of type (ι → ο) → ο be given.
Let x3 of type ι → ο be given.
Assume H3: x2 x3.
Apply H1 with
a4b00.. x2,
407b5.. x3.
Apply unknownprop_2da2b30cc490d00aa520503477db4055f9915e53389bb7c4e90a928c2e1bee3f with
x3,
x2.
The subproof is completed by applying H3.
Apply unknownprop_496f21822a3fb678f9d36a054a8a41e367bd46550d4cc9d277917362980b9e62 with
x0 (a4b00.. x2),
x2,
λ x4 : (ι → ο) → ο . x2 (3e5e9.. x4) leaving 2 subgoals.
The subproof is completed by applying L4.
Let x4 of type ι → ο be given.
Assume H5: x2 x4.
Apply unknownprop_0678ee4c4086078e18bf07d652c369b708a7ae4722dd10dfbe40c055cf9b61b7 with
x4,
λ x5 x6 : ι → ο . x2 x6.
The subproof is completed by applying H5.