Theorems · Theorem · field theory
ArchimedeanClass.stdPart_nonpos
∀ {K : Type u_1} [inst : LinearOrder K] [inst_1 : Field K] [inst_2 : IsOrderedRing K] {x : K},
x ≤ 0 → ArchimedeanClass.stdPart x ≤ 0- Defined in
- Mathlib.Algebra.Order.Ring.StandardPart
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- IsOrderedRingstatement and proof · cited by 777
- neg_nonnegproof · cited by 60
- ArchimedeanClass.stdPartstatement · cited by 42
- ArchimedeanClass.stdPart_negproof · cited by 5
- ArchimedeanClass.stdPart_nonnegproof · cited by 1
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