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

type
prop

theory
HotG

name
explicit_OrderedField_Npos_props

proof
PUa4W..

Megalodon
explicit_OrderedField_Npos_props

proofgold address
TMFBy..^{explicit_OrderedField_Npos_props}

creator
5731 Pr6Pc../4eed9..

owner
5731 Pr6Pc../4eed9..

term root
70d4a..