Proofgold Proof

Apply explicit_OrderedField_E with x0, x1, x2, x3, x4, x5, ∀ x6 : ο . (... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ ... ⟶ (∀ x7 . x7 ∈ {x8 ∈ x0|or (or (explicit_Field_minus ... ... ... ... ... ... ∈ ...) ...) ...} ⟶ ∀ x8 . x8 ∈ {x9 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x9 ∈ {x10 ∈ {x10 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x10}|x10 = x1 ⟶ ∀ x11 : ο . x11}) (x9 = x1)) (x9 ∈ {x10 ∈ {x10 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x10}|x10 = x1 ⟶ ∀ x11 : ο . x11})} ⟶ x3 x7 x8 ∈ {x9 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x9 ∈ {x10 ∈ {x10 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x10}|x10 = x1 ⟶ ∀ x11 : ο . x11}) (x9 = x1)) (x9 ∈ {x10 ∈ {x10 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x10}|x10 = x1 ⟶ ∀ x11 : ο . x11})}) ⟶ (∀ x7 . x7 ∈ {x8 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x8 ∈ {x9 ∈ {x9 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x9}|x9 = x1 ⟶ ∀ x10 : ο . x10}) (x8 = x1)) (x8 ∈ {x9 ∈ {x9 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x9}|x9 = x1 ⟶ ∀ x10 : ο . x10})} ⟶ ∀ x8 . x8 ∈ {x9 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x9 ∈ {x10 ∈ {x10 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x10}|x10 = x1 ⟶ ∀ x11 : ο . x11}) (x9 = x1)) (x9 ∈ {x10 ∈ {x10 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x10}|x10 = x1 ⟶ ∀ x11 : ο . x11})} ⟶ x4 x7 x8 ∈ {x9 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x9 ∈ {x10 ∈ {x10 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x10}|x10 = x1 ⟶ ∀ x11 : ο . x11}) (x9 = x1)) (x9 ∈ {x10 ∈ {x10 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x10}|x10 = x1 ⟶ ∀ x11 : ο . x11})}) ⟶ x6) ⟶ x6.