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Proofgold Proof

pf
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 ιιι be given.
Let x4 of type ιιι be given.
Let x5 of type ιιο be given.
Apply explicit_OrderedField_E with x0, x1, x2, x3, x4, x5, ∀ x6 : ο . ({x7 ∈ x0|explicit_OrderedField_rationalp x0 x1 x2 x3 x4 x5 x7}x0(∀ x7 . x7{x8 ∈ x0|explicit_OrderedField_rationalp x0 x1 x2 x3 x4 x5 x8}∀ x8 : ο . (x7x0∀ x9 . x9{x10 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x10{x11 ∈ {x11 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x11}|x11 = x1∀ x12 : ο . x12}) (x10 = x1)) (x10{x11 ∈ {x11 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x11}|x11 = x1∀ x12 : ο . x12})}∀ x10 . x10{x11 ∈ {x11 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x11}|x11 = x1∀ x12 : ο . x12}x4 x10 x7 = x9x8)x8)(∀ x7 . x7x0∀ 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})}∀ x9 . x9{x10 ∈ {x10 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x10}|x10 = x1∀ x11 : ο . x11}x4 x9 x7 = x8x7{x10 ∈ x0|explicit_OrderedField_rationalp x0 x1 x2 x3 x4 x5 x10})x6)x6.
Assume H0: explicit_OrderedField x0 x1 x2 x3 x4 x5.
Apply explicit_Field_E with x0, x1, x2, x3, x4, ...............∀ x6 : ο . (......(∀ x7 . ...∀ x8 . x8{x9 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x9{x10 ∈ {x10 ∈ x0|natOfOrderedField_p ... ... ... ... ... ... ...}|...}) ...) ...}∀ x9 . x9{x10 ∈ {x10 ∈ x0|natOfOrderedField_p x0 x1 x2 x3 x4 x5 x10}|x10 = x1∀ x11 : ο . x11}x4 x9 x7 = x8x7{x10 ∈ x0|explicit_OrderedField_rationalp x0 x1 x2 x3 x4 x5 x10})x6)x6.
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