Theorems · Theorem · field theory
ArchimedeanClass.stdPart_nonneg
∀ {K : Type u_1} [inst : LinearOrder K] [inst_1 : Field K] [inst_2 : IsOrderedRing K] {x : K},
0 ≤ x → 0 ≤ ArchimedeanClass.stdPart x- Defined in
- Mathlib.Algebra.Order.Ring.StandardPart
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- le_reflproof · cited by 2,061
- eq_or_neproof · cited by 1,117
- IsOrderedRingstatement and proof · cited by 777
- Eq.geproof · cited by 375
- ArchimedeanClass.mkproof · cited by 174
- ArchimedeanClass.stdPartstatement · cited by 42
- ArchimedeanClass.FiniteResidueField.mkproof · cited by 22
- OrderRingHom.compproof · cited by 15
- map_nonnegproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- ArchimedeanClass.stdPart_nonposproof · cited by 0