Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_036ece80115fe28eb061fb2c373011fdf5c8030652a5729a283dc8e51ae35651 with
59c41.. x0 x2 x4,
x1,
x3,
x5.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x6 x7 . x0 = x7.
The subproof is completed by applying unknownprop_2b9e81bf12c32fb86b330eba642b0e0334bbbea096445b11956b42c1fb97aef3 with x0, x2, x4.
Apply and3I with
x0 = x1,
x2 = x3,
x4 = x5 leaving 3 subgoals.
The subproof is completed by applying L2.
Apply unknownprop_aac02f9f6a44c6b9d39b08fc1192ca58d2ce705450eef2d9a43b23bc821d788b with
x0,
x2,
x4,
λ x6 x7 . x7 = x3.
Apply H0 with
λ x6 x7 . f482f.. x7 (4ae4a.. 4a7ef..) = x3.
Let x6 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_aac02f9f6a44c6b9d39b08fc1192ca58d2ce705450eef2d9a43b23bc821d788b with x1, x3, x5, λ x7 x8 . x6 x8 x7.
Apply unknownprop_8ca2b116f6d61bc18658d93e83637503cb39fa6349684ffefcbb8c420edb866a with
x0,
x2,
x4,
λ x6 x7 . x7 = x5.
Apply H0 with
λ x6 x7 . f482f.. x7 (4ae4a.. (4ae4a.. 4a7ef..)) = x5.
Let x6 of type ι → ι → ο be given.
The subproof is completed by applying unknownprop_8ca2b116f6d61bc18658d93e83637503cb39fa6349684ffefcbb8c420edb866a with x1, x3, x5, λ x7 x8 . x6 x8 x7.