Let x0 of type ι be given.
Let x1 of type ι → ο be given.
Let x2 of type ι → (ι → ο) → ο be given.
Let x3 of type ι be given.
Let x4 of type ι → ο be given.
Assume H1: x2 x0 x1.
Assume H2:
PNoLe x0 x1 x3 x4.
Apply unknownprop_d1cbc2e638db87d9196ef916ca16d68e66023c5a2d300e15ae355b0266749835 with
λ x5 x6 : (ι → (ι → ο) → ο) → ι → (ι → ο) → ο . x6 x2 x3 x4.
Let x5 of type ο be given.
Assume H3:
∀ x6 . and (ordinal x6) (∃ x7 : ι → ο . and (x2 x6 x7) (PNoLe x6 x7 x3 x4)) ⟶ x5.
Apply H3 with
x0.
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with
ordinal x0,
∃ x6 : ι → ο . and (x2 x0 x6) (PNoLe x0 x6 x3 x4) leaving 2 subgoals.
The subproof is completed by applying H0.
Let x6 of type ο be given.
Assume H4:
∀ x7 : ι → ο . and (x2 x0 x7) (PNoLe x0 x7 x3 x4) ⟶ x6.
Apply H4 with
x1.
Apply unknownprop_389e2fb1855352fcc964ea44fe6723d7a1c2d512f04685300e3e97621725b977 with
x2 x0 x1,
PNoLe x0 x1 x3 x4 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.