Let x0 of type ι → (ι → ι → ο) → (ι → ι → ο) → ι → 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 → ι → ο be given.
Let x4 of type ι be given.
Let x5 of type ι 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)) ⟶ x0 x1 x6 x7 x4 x5 = x0 x1 x2 x3 x4 x5.
Apply unknownprop_e30283de5e06c43feeedf7ea28f31302b2b9c54b266fa07d32b4a8647937baf2 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 . x0 x6 (2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..)))) (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = x0 x1 x2 x3 x4 x5.
Apply unknownprop_a74292f97535bb6becd1b270890a3d3a46394d140b4094c8913e6d9ae8b70b41 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 . x0 x1 (2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) x6 (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. (4ae4a.. (4ae4a.. 4a7ef..))))) = x0 x1 x2 x3 x4 x5.
Apply unknownprop_5375e18e6b66f3447ee2d8a0cd062eefda6605eebcb4137b7f34fa84355c3421 with
x1,
x2,
x3,
x4,
x5,
λ x6 x7 . x0 x1 (2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..))) (2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..)))) x4 x6 = x0 x1 x2 x3 x4 x5.
Apply H0 with
2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. 4a7ef..)),
2b2e3.. (f482f.. (0d9e7.. x1 x2 x3 x4 x5) (4ae4a.. (4ae4a.. 4a7ef..))) leaving 2 subgoals.
Let x6 of type ι be given.
Let x7 of type ι be given.
Apply unknownprop_bf3a81e508dd5bb7ebd0d922aa476a754ab01577312522215ed550d7a6c72b06 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_d478b39a50d95c7bfa6335b02cb600d8bcf61e1565ccfaa353e4998231071c0e 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 ....