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.
Apply unknownprop_022784d207f9047e5a64c6129f209ae2b30533f6c8c098dbe010367b2490a2fa with
c0301.. x0 x2,
x1,
x3.
The subproof is completed by applying H0.
Claim L2: x0 = x1
Apply L1 with
λ x4 x5 . x0 = x5.
The subproof is completed by applying unknownprop_64b30c93b63a275b33e0b1e088688090a219594d60d94e87e633646df8931180 with x0, x2.
Apply andI with
x0 = x1,
∀ x4 . prim1 x4 x0 ⟶ x2 x4 = x3 x4 leaving 2 subgoals.
The subproof is completed by applying L2.
Let x4 of type ι be given.
Apply L2 with
λ x5 x6 . prim1 x4 x5.
The subproof is completed by applying H3.
Apply unknownprop_f58b95d170c532b1a6ac682a4e91de3a8560ab9616f3c2e2f8b45045ae40523f with
x0,
x2,
x4,
λ x5 x6 . x6 = x3 x4 leaving 2 subgoals.
The subproof is completed by applying H3.
Apply H0 with
λ x5 x6 . f482f.. (f482f.. x6 (4ae4a.. 4a7ef..)) x4 = x3 x4.
Let x5 of type ι → ι → ο be given.
Apply unknownprop_f58b95d170c532b1a6ac682a4e91de3a8560ab9616f3c2e2f8b45045ae40523f with
x1,
x3,
x4,
λ x6 x7 . x5 x7 x6.
The subproof is completed by applying L4.