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 pack_e_e_0_eq with
pack_e_e 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 pack_e_e_0_eq2 with x0, x2, x4.
Apply and3I with
x0 = x1,
x2 = x3,
x4 = x5 leaving 3 subgoals.
The subproof is completed by applying L2.
Apply pack_e_e_1_eq2 with
x0,
x2,
x4,
λ x6 x7 . x7 = x3.
Apply H0 with
λ x6 x7 . ap x7 1 = x3.
Let x6 of type ι → ι → ο be given.
The subproof is completed by applying pack_e_e_1_eq2 with x1, x3, x5, λ x7 x8 . x6 x8 x7.
Apply pack_e_e_2_eq2 with
x0,
x2,
x4,
λ x6 x7 . x7 = x5.
Apply H0 with
λ x6 x7 . ap x7 2 = x5.
Let x6 of type ι → ι → ο be given.
The subproof is completed by applying pack_e_e_2_eq2 with x1, x3, x5, λ x7 x8 . x6 x8 x7.