Let x0 of type ι be given.
Let x1 of type ι → ι → ι → ι → ι → ι → ι be given.
Assume H0:
∀ x2 x3 x4 x5 x6 x7 . nth_6_tuple x0 x2 x3 x4 x5 x6 x7 = x1 x2 x3 x4 x5 x6 x7.
Apply functional extensionality with
nth_6_tuple x0,
x1.
Let x2 of type ι be given.
Apply functional extensionality with
nth_6_tuple x0 x2,
x1 x2.
Let x3 of type ι be given.
Apply functional extensionality with
nth_6_tuple x0 x2 x3,
x1 x2 x3.
Let x4 of type ι be given.
Apply functional extensionality with
nth_6_tuple x0 x2 x3 x4,
x1 x2 x3 x4.
Let x5 of type ι be given.
Apply functional extensionality with
nth_6_tuple x0 x2 x3 x4 x5,
x1 x2 x3 x4 x5.
Let x6 of type ι be given.
Apply functional extensionality with
nth_6_tuple x0 x2 x3 x4 x5 x6,
x1 x2 x3 x4 x5 x6.
Let x7 of type ι be given.
The subproof is completed by applying H0 with x2, x3, x4, x5, x6, x7.