Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ο be given.
Let x3 of type ι be given.
Assume H1: x3 ∈ x1.
Let x4 of type ι be given.
Assume H2: x4 ∈ x1.
Apply H0 with
λ x5 x6 . x2 x3 x4 = decode_r (ap x6 1) x3 x4.
Apply tuple_2_1_eq with
x1,
encode_r x1 x2,
λ x5 x6 . x2 x3 x4 = decode_r x6 x3 x4.
Let x5 of type ο → ο → ο be given.
Apply decode_encode_r with
x1,
x2,
x3,
x4,
λ x6 x7 : ο . x5 x7 x6 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.