Let x0 of type ι → ο be given.
Let x1 of type ι → ι → ι → ο be given.
Let x2 of type ι → ι be given.
Let x3 of type ι → ι → ι → ι → ι → ι be given.
Let x4 of type ι → ο be given.
Let x5 of type ι → ι → ι → ο be given.
Let x6 of type ι → ι be given.
Let x7 of type ι → ι → ι → ι → ι → ι be given.
Let x8 of type ι → ι be given.
Let x9 of type ι → ι → ι → ι be given.
Let x10 of type ι → ι be given.
Let x11 of type ι → ι → ι → ι be given.
Let x12 of type ι → ι be given.
The subproof is completed by applying andI with ∀ x13 . x0 x13 ⟶ x5 (x8 x13) (x10 x13) (x12 x13), ∀ x13 x14 x15 . x0 x13 ⟶ x0 x14 ⟶ x1 x13 x14 x15 ⟶ x7 (x8 x13) (x10 x13) (x10 x14) (x11 x13 x14 x15) (x12 x13) = x7 (x8 x13) (x8 x14) (x10 x14) (x12 x14) (x9 x13 x14 x15).