Let x0 of type ι → (ι → ι → ο) → (ι → ι → ο) → ι → ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι → ι → ο be given.
Let x4 of type ι be given.
Assume H0:
∀ x5 : ι → ι → ο . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ iff (x2 x6 x7) (x5 x6 x7)) ⟶ ∀ x6 : ι → ι → ο . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ iff (x3 x7 x8) (x6 x7 x8)) ⟶ x0 x1 x5 x6 x4 = x0 x1 x2 x3 x4.
Apply unknownprop_8056a838da97a86ae4b45f5a668b09b5d54224cecafdbbaa522039cdb61cdb64 with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x5 (2b2e3.. (f482f.. (1f7e2.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (1f7e2.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (1f7e2.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3 x4.
Apply unknownprop_b3efaa7975234558158f68aac4cbf88f3abd88ebde8cabe34c292cbf4d1900ee with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x1 (2b2e3.. (f482f.. (1f7e2.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (1f7e2.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) x5 = x0 x1 x2 x3 x4.
Apply H0 with
2b2e3.. (f482f.. (1f7e2.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
2b2e3.. (f482f.. (1f7e2.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
Let x5 of type ι be given.
Let x6 of type ι be given.
Apply unknownprop_3f14843b058ef468d228782d60bdfe824732271ba3964c94fe353c4c4bb3c45f with
x1,
x2,
x3,
x4,
x5,
x6,
λ x7 x8 : ο . iff (x2 x5 x6) x7 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x2 x5 x6.
Let x5 of type ι be given.
Let x6 of type ι be given.
Apply unknownprop_3ca258265efc0e5d7f9f9d52b4cbf8cbed02ce8da796a40e7191176f764deac7 with
x1,
x2,
x3,
x4,
x5,
x6,
λ x7 x8 : ο . iff (x3 x5 x6) x7 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x3 x5 x6.