Let x0 of type ι → (ι → ι → ι) → (ι → ι → ο) → (ι → ο) → ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ο be given.
Let x4 of type ι → ο be given.
Assume H0:
∀ x5 : ι → ι → ι . (∀ x6 . prim1 x6 x1 ⟶ ∀ x7 . prim1 x7 x1 ⟶ 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)) ⟶ ∀ x7 : ι → ο . (∀ x8 . prim1 x8 x1 ⟶ iff (x4 x8) (x7 x8)) ⟶ x0 x1 x5 x6 x7 = x0 x1 x2 x3 x4.
Apply unknownprop_b0f82d1c69f380550644ef11c2dd41f9d5d4f492a768abdd3d6e9adfd74b9c76 with
x1,
x2,
x3,
x4,
λ x5 x6 . x0 x5 (e3162.. (f482f.. (0fd05.. x1 x2 x3 x4) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (0fd05.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (0fd05.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = x0 x1 x2 x3 x4.
Apply H0 with
e3162.. (f482f.. (0fd05.. x1 x2 x3 x4) (4ae4a.. 4a7ef..)),
2b2e3.. (f482f.. (0fd05.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. 4a7ef..))),
decode_p (f482f.. (0fd05.. x1 x2 x3 x4) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) leaving 3 subgoals.
The subproof is completed by applying unknownprop_fed6cf07aa814164a3daa084792cf9b08a4358b581f07c8eb65ac4ff36c71f64 with x1, x2, x3, x4.
Let x5 of type ι be given.
Let x6 of type ι be given.
Apply unknownprop_5ea683a46d4420d1129d98b68c2d8a411e60a35ab8618f29559598685876fec4 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.
Let x5 of type ι be given.
Apply unknownprop_47bb3b8d7a71a1e8960090c3da1b97fe4880f40eb7b56b3243c5a95be7978365 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 : ο . iff (x4 x5) x6 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x4 x5.