Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Let x3 of type ι → ι → ι be given.
Let x4 of type ι → ι → ι be given.
Let x5 of type ι → ι → ο be given.
Assume H1:
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x5 x6 x7 ⟶ x5 x7 x8 ⟶ x5 x6 x8.
Assume H2:
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ iff (and (x5 x6 x7) (x5 x7 x6)) (x6 = x7).
Assume H3:
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ or (x5 x6 x7) (x5 x7 x6).
Assume H4:
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x5 x6 x7 ⟶ x5 (x3 x6 x8) (x3 x7 x8).
Assume H5:
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x5 x1 x6 ⟶ x5 x1 x7 ⟶ x5 x1 (x4 x6 x7).
Apply and6I with
explicit_Field x0 x1 x2 x3 x4,
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x5 x6 x7 ⟶ x5 x7 x8 ⟶ x5 x6 x8,
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ iff (and (x5 x6 x7) (x5 x7 x6)) (x6 = x7),
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ or (x5 x6 x7) (x5 x7 x6),
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ ∀ x8 . prim1 x8 x0 ⟶ x5 x6 x7 ⟶ x5 (x3 x6 x8) (x3 x7 x8),
∀ x6 . prim1 x6 x0 ⟶ ∀ x7 . prim1 x7 x0 ⟶ x5 x1 x6 ⟶ x5 x1 x7 ⟶ x5 x1 (x4 x6 x7) leaving 6 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.