Let x0 of type ι → ((ι → ο) → ο) → (ι → ο) → ι be given.
Let x1 of type ι be given.
Let x2 of type (ι → ο) → ο be given.
Let x3 of type ι → ο be given.
Assume H0:
∀ x4 : (ι → ο) → ο . (∀ x5 : ι → ο . (∀ x6 . x5 x6 ⟶ prim1 x6 x1) ⟶ iff (x2 x5) (x4 x5)) ⟶ ∀ x5 : ι → ο . (∀ x6 . prim1 x6 x1 ⟶ iff (x3 x6) (x5 x6)) ⟶ x0 x1 x4 x5 = x0 x1 x2 x3.
Apply unknownprop_6d2dce7078e61066802501dd67fa0f8d1d04bdbc9f24e77dcf05cf9a71e757b2 with
x1,
x2,
x3,
λ x4 x5 . x0 x4 (decode_c (f482f.. (01d88.. x1 x2 x3) (4ae4a.. 4a7ef..))) (decode_p (f482f.. (01d88.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..)))) = x0 x1 x2 x3.
Apply H0 with
decode_c (f482f.. (01d88.. x1 x2 x3) (4ae4a.. 4a7ef..)),
decode_p (f482f.. (01d88.. x1 x2 x3) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
Let x4 of type ι → ο be given.
Assume H1:
∀ x5 . x4 x5 ⟶ prim1 x5 x1.
Apply unknownprop_ed29eb2a3dee7023c289bdb42a804e4893144f032afd50419f3fc25fc78c2df2 with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x2 x4) x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x2 x4.
Let x4 of type ι be given.
Apply unknownprop_b158b7086827b8c679d5ced1a07e0e8b2c2264c4046da20f1d53c64aab107031 with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x3 x4) x5 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x3 x4.