Let x0 of type ι → (ι → ι → ο) → ι → ο be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι be given.
Assume H0:
∀ x4 : ι → ι → ο . (∀ x5 . prim1 x5 x1 ⟶ ∀ x6 . prim1 x6 x1 ⟶ iff (x2 x5 x6) (x4 x5 x6)) ⟶ x0 x1 x4 x3 = x0 x1 x2 x3.
Apply unknownprop_80b971e1e769c036da944ad596d7d907ce651d9af374e9c7a1d04d6f88668c42 with
x1,
x2,
x3,
λ x4 x5 . x0 x4 (2b2e3.. (f482f.. (dd3c8.. x1 x2 x3) (4ae4a.. 4a7ef..))) (f482f.. (dd3c8.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) = x0 x1 x2 x3.
Apply unknownprop_f1e6338dba9d8a4b13d4526138bc59bec058c063c6bea746ef372dfd89320783 with
x1,
x2,
x3,
λ x4 x5 . x0 x1 (2b2e3.. (f482f.. (dd3c8.. x1 x2 x3) (4ae4a.. 4a7ef..))) x4 = x0 x1 x2 x3.
Apply H0 with
2b2e3.. (f482f.. (dd3c8.. x1 x2 x3) (4ae4a.. 4a7ef..)).
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_99ef3c56c8cdbdbdd0c30f3ff13386c5db4ed206a6215787f09bd20975ed1342 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x2 x4 x5) x6 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 x4 x5.