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 → ο be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Assume H1: x5 ∈ x1.
Let x6 of type ι be given.
Assume H2: x6 ∈ x1.
Apply H0 with
λ x7 x8 . x2 x5 x6 = decode_r (ap x8 1) x5 x6.
Apply tuple_4_1_eq with
x1,
encode_r x1 x2,
Sep x1 x3,
x4,
λ x7 x8 . x2 x5 x6 = decode_r x8 x5 x6.
Let x7 of type ο → ο → ο be given.
Apply decode_encode_r with
x1,
x2,
x5,
x6,
λ x8 x9 : ο . x7 x9 x8 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.