Let x0 of type ι → (ι → ο) → ο be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι → ο be given.
Let x4 of type ι → ο be given.
Apply H2 with
8356a.. x0 x2 x4.
Let x5 of type ι be given.
Apply H4 with
8356a.. x0 x2 x4.
Assume H6:
∃ x6 : ι → ο . and (x0 x5 x6) (35b9b.. x1 x3 x5 x6).
Apply H6 with
8356a.. x0 x2 x4.
Let x6 of type ι → ο be given.
Assume H7:
(λ x7 : ι → ο . and (x0 x5 x7) (35b9b.. x1 x3 x5 x7)) x6.
Apply H7 with
8356a.. x0 x2 x4.
Assume H8: x0 x5 x6.
Let x7 of type ο be given.
Assume H10:
∀ x8 . and (ordinal x8) (∃ x9 : ι → ο . and (x0 x8 x9) (35b9b.. x2 x4 x8 x9)) ⟶ x7.
Apply H10 with
x5.
Apply andI with
ordinal x5,
∃ x8 : ι → ο . and (x0 x5 x8) (35b9b.. x2 x4 x5 x8) leaving 2 subgoals.
The subproof is completed by applying H5.
Let x8 of type ο be given.
Assume H11:
∀ x9 : ι → ο . and (x0 x5 x9) (35b9b.. x2 x4 x5 x9) ⟶ x8.
Apply H11 with
x6.
Apply andI with
x0 x5 x6,
35b9b.. x2 x4 x5 x6 leaving 2 subgoals.
The subproof is completed by applying H8.
Apply unknownprop_e2fba515d4f4b73abb6664acd434e29949a2b63c3796bbc956c77c7f4dcece18 with
x2,
x1,
x5,
x4,
x3,
x6 leaving 5 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
The subproof is completed by applying H5.
The subproof is completed by applying H3.
The subproof is completed by applying H9.