Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = pack_p (ap x1 0) (decode_p (ap x1 1)).
Let x1 of type ι be given.
Let x2 of type ι → ο be given.
Apply pack_p_0_eq2 with
x1,
x2,
λ x3 x4 . pack_p x1 x2 = pack_p x3 (decode_p (ap (pack_p x1 x2) 1)).
Apply pack_p_ext with
x1,
x2,
decode_p (ap (pack_p x1 x2) 1).
Let x3 of type ι be given.
Assume H1: x3 ∈ x1.
Apply pack_p_1_eq2 with
x1,
x2,
x3,
λ x4 x5 : ο . iff (x2 x3) x4 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying iff_refl with x2 x3.