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.
Apply pack_e_0_eq with
pack_e 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 pack_e_0_eq2 with x0, x2.
Apply andI with
x0 = x1,
x2 = x3 leaving 2 subgoals.
The subproof is completed by applying L2.
Apply pack_e_1_eq2 with
x0,
x2,
λ x4 x5 . x5 = x3.
Apply H0 with
λ x4 x5 . ap x5 1 = x3.
Let x4 of type ι → ι → ο be given.
The subproof is completed by applying pack_e_1_eq2 with x1, x3, λ x5 x6 . x4 x6 x5.