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.
Apply explicit_OrderedField_E with
x0,
x1,
x2,
x3,
x4,
x5,
∀ x6 . x6 ⊆ x0 ⟶ x1 ∈ x6 ⟶ x2 ∈ x6 ⟶ (∀ x7 . x7 ∈ x6 ⟶ ∀ x8 . x8 ∈ x6 ⟶ x3 x7 x8 ∈ x6) ⟶ (∀ x7 . x7 ∈ x6 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x7 ∈ x6) ⟶ (∀ x7 . x7 ∈ x6 ⟶ ∀ x8 . x8 ∈ x6 ⟶ x4 x7 x8 ∈ x6) ⟶ (∀ x7 . x7 ∈ x6 ⟶ (x7 = x1 ⟶ ∀ x8 : ο . x8) ⟶ ∃ x8 . and (x8 ∈ x6) (x4 x7 x8 = x2)) ⟶ explicit_OrderedField x6 x1 x2 x3 x4 x5.
Apply explicit_Field_E with
x0,
x1,
x2,
x3,
x4,
(∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x5 x6 x7 ⟶ x5 x7 x8 ⟶ x5 x6 x8) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ iff (and (x5 x6 x7) (x5 x7 x6)) (x6 = x7)) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ or (x5 x6 x7) (x5 x7 x6)) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ ∀ x8 . x8 ∈ x0 ⟶ x5 x6 x7 ⟶ x5 (x3 x6 x8) (x3 x7 x8)) ⟶ (∀ x6 . x6 ∈ x0 ⟶ ∀ x7 . x7 ∈ x0 ⟶ x5 x1 x6 ⟶ x5 x1 x7 ⟶ x5 x1 (x4 x6 x7)) ⟶ ∀ x6 . x6 ⊆ x0 ⟶ x1 ∈ x6 ⟶ x2 ∈ x6 ⟶ (∀ x7 . x7 ∈ x6 ⟶ ∀ x8 . x8 ∈ x6 ⟶ x3 x7 x8 ∈ x6) ⟶ (∀ x7 . x7 ∈ x6 ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x7 ∈ x6) ⟶ (∀ x7 . x7 ∈ x6 ⟶ ∀ x8 . x8 ∈ x6 ⟶ x4 x7 x8 ∈ x6) ⟶ (∀ x7 . x7 ∈ x6 ⟶ (x7 = x1 ⟶ ∀ x8 : ο . x8) ⟶ ∃ x8 . and (x8 ∈ x6) (x4 x7 x8 = x2)) ⟶ explicit_OrderedField x6 x1 x2 x3 x4 x5.
Assume H2: ∀ x6 . ... ⟶ ∀ x7 . ... ⟶ x3 ... ... ∈ ....