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.
Let x6 of type ι be given.
Let x7 of type ι be given.
Let x8 of type ι be given.
Let x9 of type ι → ι → ι be given.
Let x10 of type ι → ι → ι be given.
Let x11 of type ι → ι → ο be given.
Let x12 of type ι → ι be given.
Apply explicit_Reals_E with
x0,
x1,
x2,
x3,
x4,
x5,
bij x0 x6 x12 ⟶ x12 x1 = x7 ⟶ x12 x2 = x8 ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ x12 (x3 x13 x14) = x9 (x12 x13) (x12 x14)) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ x12 (x4 x13 x14) = x10 (x12 x13) (x12 x14)) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ iff (x5 x13 x14) (x11 (x12 x13) (x12 x14))) ⟶ explicit_Reals x6 x7 x8 x9 x10 x11.
Apply explicit_OrderedField_E with
x0,
x1,
x2,
x3,
x4,
x5,
(∀ x13 . ... ⟶ ∀ x14 . ... ⟶ ... ⟶ ... ⟶ ∃ x15 . and (... ∈ ...) ...) ⟶ (∀ x13 . x13 ∈ setexp x0 (Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)) ⟶ ∀ x14 . x14 ∈ setexp x0 (Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)) ⟶ (∀ x15 . x15 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5) ⟶ and (and (x5 (ap x13 x15) (ap x14 x15)) (x5 (ap x13 x15) (ap x13 (x3 x15 x2)))) (x5 (ap x14 (x3 x15 x2)) (ap x14 x15))) ⟶ ∃ x15 . and (x15 ∈ x0) (∀ x16 . x16 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5) ⟶ and (x5 (ap x13 x16) x15) (x5 x15 (ap x14 x16)))) ⟶ bij x0 x6 x12 ⟶ x12 x1 = x7 ⟶ x12 x2 = x8 ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ x12 (x3 x13 x14) = x9 (x12 x13) (x12 x14)) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ x12 (x4 x13 x14) = x10 (x12 x13) (x12 x14)) ⟶ (∀ x13 . x13 ∈ x0 ⟶ ∀ x14 . x14 ∈ x0 ⟶ iff (x5 x13 x14) (x11 (x12 x13) (x12 x14))) ⟶ explicit_Reals x6 x7 x8 x9 x10 x11.