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 → ο be given.
Let x5 of type ι be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Assume H1: x7 ∈ x1.
Let x8 of type ι be given.
Assume H2: x8 ∈ x1.
Apply H0 with
λ x9 x10 . x3 x7 x8 = decode_b (ap x10 2) x7 x8.
Apply tuple_6_2_eq with
x1,
encode_b x1 x2,
encode_b x1 x3,
encode_r x1 x4,
x5,
x6,
λ x9 x10 . x3 x7 x8 = decode_b x10 x7 x8.
Let x9 of type ι → ι → ο be given.
Apply decode_encode_b with
x1,
x3,
x7,
x8,
λ x10 x11 . x9 x11 x10 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.