Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Apply unknownprop_9f372588b2ceb8f59c01197f59d9126b3b6e4d0384005a5ae4b3ac804ebc30d1 with
8eacd.. 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_128401b26ca0bc08d54bfca9904ebdbf186db1274a4be846be9a9cc30eb990c9 with x0, x2, x4.
Apply and3I with
x0 = x1,
∀ x6 . prim1 x6 x0 ⟶ x2 x6 = x3 x6,
x4 = x5 leaving 3 subgoals.
The subproof is completed by applying L2.
Let x6 of type ι be given.
Apply unknownprop_185dfaf856c8b7f2b4591a434b0b04e8904e3e58c14681f42a4c6a9bacc9a6c3 with
x0,
x2,
x4,
x6,
λ x7 x8 . x8 = x3 x6 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply L2 with
λ x7 x8 . prim1 x6 x7.
The subproof is completed by applying H3.
Apply H0 with
λ x7 x8 . f482f.. (f482f.. x8 (4ae4a.. 4a7ef..)) x6 = x3 x6.
Let x7 of type ι → ι → ο be given.
Apply unknownprop_185dfaf856c8b7f2b4591a434b0b04e8904e3e58c14681f42a4c6a9bacc9a6c3 with
x1,
x3,
x5,
x6,
λ x8 x9 . x7 x9 x8.
The subproof is completed by applying L4.
Apply unknownprop_e852dd30a45cb3a8cce74800ccca965088221e00f4794a6d5a0a5270b65d5a2a 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_e852dd30a45cb3a8cce74800ccca965088221e00f4794a6d5a0a5270b65d5a2a with x1, x3, x5, λ x7 x8 . x6 x8 x7.