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 be given.
Let x6 of type ι be given.
Let x7 of type ι be given.
Let x8 of type ι → ι → ι be given.
Let x9 of type ι → ι → ι be given.
Let x10 of type ι → ι be given.
Apply explicit_Field_E with
x0,
x1,
x2,
x3,
x4,
bij x0 x5 x10 ⟶ x10 x1 = x6 ⟶ x10 x2 = x7 ⟶ (∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ x10 (x3 x11 x12) = x8 (x10 x11) (x10 x12)) ⟶ (∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ x10 (x4 x11 x12) = x9 (x10 x11) (x10 x12)) ⟶ explicit_Field x5 x6 x7 x8 x9.
Assume H1: ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ x3 x11 x12 ∈ x0.
Assume H2: ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ x3 x11 (x3 x12 x13) = x3 (x3 x11 x12) x13.
Assume H3: ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ x3 x11 x12 = x3 x12 x11.
Assume H4: x1 ∈ x0.
Assume H5: ∀ x11 . x11 ∈ x0 ⟶ x3 x1 x11 = x11.
Assume H6:
∀ x11 . x11 ∈ x0 ⟶ ∃ x12 . and (x12 ∈ x0) (x3 x11 x12 = x1).
Assume H7: ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ x4 x11 x12 ∈ x0.
Assume H8: ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ x4 x11 (x4 x12 x13) = x4 (x4 x11 x12) x13.
Assume H9: ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ x4 x11 x12 = x4 x12 x11.
Assume H10: x2 ∈ x0.
Assume H11: x2 = x1 ⟶ ∀ x11 : ο . x11.
Assume H12: ∀ x11 . x11 ∈ x0 ⟶ x4 x2 x11 = x11.
Assume H13:
∀ x11 . x11 ∈ x0 ⟶ (x11 = x1 ⟶ ∀ x12 : ο . x12) ⟶ ∃ x12 . and (x12 ∈ x0) (x4 x11 x12 = x2).
Assume H14: ∀ x11 . x11 ∈ x0 ⟶ ∀ x12 . x12 ∈ x0 ⟶ ∀ x13 . x13 ∈ x0 ⟶ x4 x11 (x3 x12 x13) = x3 (x4 x11 x12) (x4 x11 x13).
Assume H15:
bij x0 x5 x10.
Assume H16: x10 x1 = x6.