Proofgold Proposition

∀ x0 x1 x2 . ∀ x3 x4 : ι → ι → ι . ∀ x5 : ι → ι → ο . explicit_OrderedField x0 x1 x2 x3 x4 x5 ⟶ ∀ x6 : ο . ((∀ x7 . x7 ∈ {x8 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x8 = x1 ⟶ ∀ x9 : ο . x9} ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x7 ∈ {x8 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x8 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10}) (x8 = x1)) (x8 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10})}) ⟶ x1 ∈ {x7 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x7 ∈ {x8 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x8 = x1 ⟶ ∀ x9 : ο . x9}) (x7 = x1)) (x7 ∈ {x8 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x8 = x1 ⟶ ∀ x9 : ο . x9})} ⟶ {x7 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x7 = x1 ⟶ ∀ x8 : ο . x8} ⊆ {x7 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x7 ∈ {x8 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x8 = x1 ⟶ ∀ x9 : ο . x9}) (x7 = x1)) (x7 ∈ {x8 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x8 = x1 ⟶ ∀ x9 : ο . x9})} ⟶ {x7 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x7 ∈ {x8 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x8 = x1 ⟶ ∀ x9 : ο . x9}) (x7 = x1)) (x7 ∈ {x8 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x8 = x1 ⟶ ∀ x9 : ο . x9})} ⊆ x0 ⟶ (∀ x7 . x7 ∈ {x8 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x8 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10}) (x8 = x1)) (x8 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10})} ⟶ ∀ x8 : ο . (explicit_Field_minus x0 x1 x2 x3 x4 x7 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10} ⟶ x8) ⟶ (x7 = x1 ⟶ x8) ⟶ (x7 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10} ⟶ x8) ⟶ x8) ⟶ x2 ∈ {x7 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x7 ∈ {x8 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x8 = x1 ⟶ ∀ x9 : ο . x9}) (x7 = x1)) (x7 ∈ {x8 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x8 = x1 ⟶ ∀ x9 : ο . x9})} ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x2 ∈ {x7 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x7 ∈ {x8 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x8 = x1 ⟶ ∀ x9 : ο . x9}) (x7 = x1)) (x7 ∈ {x8 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x8 = x1 ⟶ ∀ x9 : ο . x9})} ⟶ (∀ x7 . x7 ∈ {x8 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x8 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10}) (x8 = x1)) (x8 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10})} ⟶ explicit_Field_minus x0 x1 x2 x3 x4 x7 ∈ {x8 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x8 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10}) (x8 = x1)) (x8 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10})}) ⟶ (∀ x7 . x7 ∈ {x8 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x8 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10}) (x8 = x1)) (x8 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10})} ⟶ ∀ x8 . x8 ∈ {x9 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x9 ∈ {x10 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x10 = x1 ⟶ ∀ x11 : ο . x11}) (x9 = x1)) (x9 ∈ {x10 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x10 = x1 ⟶ ∀ x11 : ο . x11})} ⟶ x3 x7 x8 ∈ {x9 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x9 ∈ {x10 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x10 = x1 ⟶ ∀ x11 : ο . x11}) (x9 = x1)) (x9 ∈ {x10 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x10 = x1 ⟶ ∀ x11 : ο . x11})}) ⟶ (∀ x7 . x7 ∈ {x8 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x8 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10}) (x8 = x1)) (x8 ∈ {x9 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x9 = x1 ⟶ ∀ x10 : ο . x10})} ⟶ ∀ x8 . x8 ∈ {x9 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x9 ∈ {x10 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x10 = x1 ⟶ ∀ x11 : ο . x11}) (x9 = x1)) (x9 ∈ {x10 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x10 = x1 ⟶ ∀ x11 : ο . x11})} ⟶ x4 x7 x8 ∈ {x9 ∈ x0|or (or (explicit_Field_minus x0 x1 x2 x3 x4 x9 ∈ {x10 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x10 = x1 ⟶ ∀ x11 : ο . x11}) (x9 = x1)) (x9 ∈ {x10 ∈ Sep x0 (natOfOrderedField_p x0 x1 x2 x3 x4 x5)|x10 = x1 ⟶ ∀ x11 : ο . x11})}) ⟶ x6) ⟶ x6

type
prop

theory
HotG

name
explicit_OrderedField_Z_props

proof
PUa4W..

Megalodon
explicit_OrderedField_Z_props

proofgold address
TMdyX..^{explicit_OrderedField_Z_props}

creator
5731 Pr6Pc../0140b..

owner
5731 Pr6Pc../0140b..

term root
c4e83..