Let x0 of type ι → (ι → ι → ο) → (ι → ι → ο) → (ι → ο) → (ι → ο) → ο 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 → ο be given.
Let x5 of type ι → ο be given.
Assume H0:
∀ x6 : ι → ι → ο . (∀ x7 . prim1 x7 x1 ⟶ ∀ x8 . prim1 x8 x1 ⟶ iff (x2 x7 x8) (x6 x7 x8)) ⟶ ∀ x7 : ι → ι → ο . (∀ x8 . prim1 x8 x1 ⟶ ∀ x9 . prim1 x9 x1 ⟶ iff (x3 x8 x9) (x7 x8 x9)) ⟶ ∀ x8 : ι → ο . (∀ x9 . prim1 x9 x1 ⟶ iff (x4 x9) (x8 x9)) ⟶ ∀ x9 : ι → ο . (∀ x10 . prim1 x10 x1 ⟶ iff (x5 x10) (x9 x10)) ⟶ x0 x1 x6 x7 x8 x9 = x0 x1 x2 x3 x4 x5.
Apply unknownprop_e14f7b429713336ceac3b91fcc55de4fd9e42dd95788cd866fa2797941b492ab with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 . x0 x6 (2b2e3.. (f482f.. (918ae.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (918ae.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (decode_p (f482f.. (918ae.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) (decode_p (f482f.. (918ae.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))))) = x0 x1 x2 x3 x4 x5.
Apply H0 with
2b2e3.. (f482f.. (918ae.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)),
2b2e3.. (f482f.. (918ae.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))),
decode_p (f482f.. (918ae.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))),
decode_p (f482f.. (918ae.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) leaving 4 subgoals.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_cd7491bb8277007bfb56f5d7e42be1c59cf6fcef57810a06095df2bae5eb9892 with
x1,
x2,
x3,
x4,
x5,
x6,
x7,
λ x8 x9 : ο . iff (x2 x6 x7) x8 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 x6 x7.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_6640545361000e8f24742fa000eaa7c62a3116e5b9874bad2064ad6e701740ae with
x1,
x2,
x3,
x4,
x5,
x6,
x7,
λ x8 x9 : ο . iff (x3 x6 x7) x8 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 x6 x7.
Let x6 of type ι be given.
Apply unknownprop_4891b05184c55b25fe37e0d500db5a0f66499846c5ede105e100f75de8266e46 with
x1,
x2,
x3,
x4,
x5,
x6,
λ x7 x8 : ο . iff (x4 x6) x7 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x4 x6.
Let x6 of type ι be given.
Apply unknownprop_29343dedcc828a3fa4de9834f1f575dedf93c15d1f3513126d29c19faad30238 with
x1,
x2,
x3,
x4,
x5,
x6,
λ x7 x8 : ο . iff (x5 x6) x7 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x5 x6.