Let x0 of type ι be given.
Apply H0 with
λ x1 . x1 = pack_r (ap x1 0) (decode_r (ap x1 1)).
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Apply pack_r_0_eq2 with
x1,
x2,
λ x3 x4 . pack_r x1 x2 = pack_r x3 (decode_r (ap (pack_r x1 x2) 1)).
Apply pack_r_ext with
x1,
x2,
decode_r (ap (pack_r x1 x2) 1).
Let x3 of type ι be given.
Assume H1: x3 ∈ x1.
Let x4 of type ι be given.
Assume H2: x4 ∈ x1.
Apply pack_r_1_eq2 with
x1,
x2,
x3,
x4,
λ x5 x6 : ο . iff (x2 x3 x4) x5 leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying iff_refl with x2 x3 x4.