Let x0 of type (CT2 (CT2 (ι → ι → ι))) → ι → ι → ι be given.
Assume H0:
∀ x1 : ((((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . 403c9.. x1 ⟶ fb516.. (x0 x1).
Apply unknownprop_fab341239b745c35a31d9a39af165a59f3b7bf553f09b5e965a8b76d704c99fb with
λ x1 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . 36e15.. (λ x2 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x0 (λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 x1 x2)),
λ x1 x2 : ο . x2 = ∀ x3 : ((((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . 403c9.. x3 ⟶ 6fb7f.. (x0 x3) leaving 2 subgoals.
The subproof is completed by applying L1.
Apply prop_ext_2 with
∀ x1 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . 64789.. x1 ⟶ 6fb7f.. (36e15.. (λ x2 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x0 (λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 x1 x2))),
∀ x1 : ((((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . 403c9.. x1 ⟶ 6fb7f.. (x0 x1) leaving 2 subgoals.
Assume H2:
∀ x1 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . 64789.. x1 ⟶ 6fb7f.. (36e15.. (λ x2 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x0 (λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 x1 x2))).
Let x1 of type CT2 (CT2 (ι → ι → ι)) be given.
Apply H3 with
6fb7f.. (x0 x1).
Assume H4:
and (x1 = λ x2 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x2 (x1 (λ x3 x4 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3)) (x1 (λ x3 x4 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4))) (64789.. (x1 (λ x2 x3 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x2))).
Apply H4 with
64789.. (x1 (λ x2 x3 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3)) ⟶ 6fb7f.. (x0 x1).
Assume H5: x1 = λ x2 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x2 (x1 (λ x3 x4 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3)) (x1 (λ x3 x4 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4)).
Assume H6:
64789.. (x1 (λ x2 x3 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x2)).
Assume H7:
64789.. (x1 (λ x2 x3 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3)).
Apply H5 with
λ x2 x3 : ((((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . 6fb7f.. (x0 x3).
Claim L8:
6fb7f.. (36e15.. (λ x2 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x0 (λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 (x1 (λ x4 x5 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4)) x2)))Apply H2 with
x1 (λ x2 x3 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x2).
The subproof is completed by applying H6.
Claim L9:
∀ x2 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . 64789.. x2 ⟶ fb516.. (x0 (λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 (x1 (λ x4 x5 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4)) x2))Let x2 of type CT2 (ι → ι → ι) be given.
Apply H0 with
λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 (x1 (λ x4 x5 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4)) x2.
Apply and3I with
(λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 (x1 (λ x4 x5 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4)) x2) = λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 (x1 (λ x4 x5 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4)) x2,
64789.. (x1 (λ x3 x4 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3)),
64789.. x2 leaving 3 subgoals.
Let x3 of type (CT2 (CT2 (ι → ι → ι))) → (CT2 (CT2 (ι → ι → ι))) → ο be given.
Assume H10: x3 (λ x4 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4 (x1 (λ x5 x6 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x5)) x2) (λ x4 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4 (x1 (λ x5 x6 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x5)) x2).
The subproof is completed by applying H10.
The subproof is completed by applying H6.
The subproof is completed by applying H9.
Claim L10:
∀ x2 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . 64789.. x2 ⟶ 6fb7f.. (x0 (λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 (x1 (λ x4 x5 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4)) x2))Apply unknownprop_fab341239b745c35a31d9a39af165a59f3b7bf553f09b5e965a8b76d704c99fb with
λ x2 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x0 (λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 (x1 (λ x4 x5 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4)) x2),
λ x2 x3 : ο . x2 leaving 2 subgoals.
The subproof is completed by applying L9.
The subproof is completed by applying L8.
Apply L10 with
x1 (λ x2 x3 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3).
The subproof is completed by applying H7.
Assume H2:
∀ x1 : ((((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . 403c9.. x1 ⟶ 6fb7f.. (x0 x1).
Let x1 of type CT2 (ι → ι → ι) be given.
Apply unknownprop_fab341239b745c35a31d9a39af165a59f3b7bf553f09b5e965a8b76d704c99fb with
λ x2 : ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x0 (λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 x1 x2),
λ x2 x3 : ο . x3 leaving 2 subgoals.
The subproof is completed by applying L4.
Let x2 of type CT2 (ι → ι → ι) be given.
Apply H2 with
λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 x1 x2.
Apply and3I with
(λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 x1 x2) = λ x3 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x3 x1 x2,
64789.. x1,
64789.. x2 leaving 3 subgoals.
Let x3 of type (CT2 (CT2 (ι → ι → ι))) → (CT2 (CT2 (ι → ι → ι))) → ο be given.
Assume H6: x3 (λ x4 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4 x1 x2) (λ x4 : (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → (((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι) → ((ι → ι → ι) → (ι → ι → ι) → ι → ι → ι) → ι → ι → ι . x4 x1 x2).
The subproof is completed by applying H6.