Let x0 of type ι be given.
Let x1 of type ι → ι be given.
Let x2 of type ι → ι be given.
Let x3 of type ι be given.
Let x4 of type ι be given.
Let x5 of type ι be given.
Let x6 of type ι → ι → ι be given.
Let x7 of type ι → ι → ι be given.
Assume H1:
∃ x8 : ι → ι → ο . 62ee1.. (1216a.. x0 (λ x9 . x1 x9 = x9)) x3 x4 x6 x7 x8.
Assume H6:
∀ x8 . prim1 x8 x0 ⟶ x8 = x6 (x1 x8) (x7 x5 (x2 x8)).
Assume H7:
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x1 x8 = x1 x9 ⟶ x2 x8 = x2 x9 ⟶ x8 = x9.
Assume H8: x6 (x7 x5 x5) x4 = x3.
Apply and7I with
and (and (explicit_Field x0 x3 x4 x6 x7) (∃ x8 : ι → ι → ο . 62ee1.. (1216a.. x0 (λ x9 . x1 x9 = x9)) x3 x4 x6 x7 x8)) (∀ x8 . prim1 x8 x0 ⟶ prim1 (x2 x8) (1216a.. x0 (λ x9 . x1 x9 = x9))),
prim1 x5 x0,
∀ x8 . prim1 x8 x0 ⟶ prim1 (x1 x8) x0,
∀ x8 . prim1 x8 x0 ⟶ prim1 (x2 x8) x0,
∀ x8 . prim1 x8 x0 ⟶ x8 = x6 (x1 x8) (x7 x5 (x2 x8)),
∀ x8 . prim1 x8 x0 ⟶ ∀ x9 . prim1 x9 x0 ⟶ x1 x8 = x1 x9 ⟶ x2 x8 = x2 x9 ⟶ x8 = x9,
x6 (x7 x5 x5) x4 = x3 leaving 7 subgoals.
Apply and3I with
explicit_Field x0 x3 x4 x6 x7,
∃ x8 : ι → ι → ο . 62ee1.. (1216a.. x0 (λ x9 . x1 x9 = x9)) x3 x4 x6 x7 x8,
∀ x8 . prim1 x8 x0 ⟶ prim1 (x2 x8) (1216a.. x0 (λ x9 . x1 x9 = x9)) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
The subproof is completed by applying H4.
The subproof is completed by applying H5.
The subproof is completed by applying H6.
The subproof is completed by applying H7.
The subproof is completed by applying H8.