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Theorems · Theorem · field theory

ArchimedeanClass.stdPart_of_mk_ne_zero

∀ {K : Type u_1} [inst : LinearOrder K] [inst_1 : Field K] [inst_2 : IsOrderedRing K] {x : K},
  ArchimedeanClass.mk x ≠ 0 → ArchimedeanClass.stdPart x = 0

Alias of the reverse direction of ArchimedeanClass.stdPart_eq_zero.

Defined in
Mathlib.Algebra.Order.Ring.StandardPart
Cited by
4 results in Mathlib
Foundations
Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
LinearOrderFieldIsOrderedRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ArchimedeanClass.stdPart_inv · cited by 2ArchimedeanClass.stdPart_…ArchimedeanClass.stdPart_add_eq_right · cited by 2ArchimedeanClass.stdPart_…ArchimedeanClass.stdPart_nonneg · cited by 1ArchimedeanClass.stdPart_…ArchimedeanClass.stdPart_eq_sInf · cited by 1ArchimedeanClass.stdPart_…Real · cited by 25697RealLinearOrder · cited by 8572LinearOrderField · cited by 7404FieldIsOrderedRing · cited by 777IsOrderedRingArchimedeanClass · cited by 247ArchimedeanClassArchimedeanClass.mk · cited by 174ArchimedeanClass.mkArchimedeanClass.stdPart · cited by 42ArchimedeanClass.stdPartArchimedeanClass.stdPart_eq_zero · cited by 6ArchimedeanClass.stdPart_…ArchimedeanClass.stdPart_of_m…CITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.