Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι → ι → ι be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι → ι be given.
Let x5 of type ι → ι → ο be given.
Let x6 of type ι be given.
Assume H1: x6 ∈ x1.
Let x7 of type ι be given.
Assume H2: x7 ∈ x1.
Apply H0 with
λ x8 x9 . x3 x6 x7 = decode_b (ap x9 2) x6 x7.
Apply tuple_5_2_eq with
x1,
encode_b x1 x2,
encode_b x1 x3,
lam x1 x4,
encode_r x1 x5,
λ x8 x9 . x3 x6 x7 = decode_b x9 x6 x7.
Let x8 of type ι → ι → ο be given.
Apply decode_encode_b with
x1,
x3,
x6,
x7,
λ x9 x10 . x8 x10 x9 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.