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Theorems · Definition · logic and foundations

Hyperreal.IsSt

Deprecated since 2026-01-05Use ArchimedeanClass.stdPart instead.

ℝ* → ℝ → Prop

Standard part predicate. Do not use. This is equivalent to the conjunction of 0 ≤ ArchimedeanClass.mk x and ArchimedeanClass.stdPart x = r.

Defined in
Mathlib.Analysis.Real.Hyperreal
Cited by
42 results in Mathlib
Foundations
Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Hyperreal.Infinitesimal · cited by 41Hyperreal.InfinitesimalHyperreal.st · cited by 16Hyperreal.stHyperreal.isSt_ofSeq_iff_tendsto · cited by 7Hyperreal.isSt_ofSeq_iff_…Hyperreal.isSt_refl_real · cited by 7Hyperreal.isSt_refl_realHyperreal.isSt_st' · cited by 7Hyperreal.isSt_st'Hyperreal.IsSt.unique · cited by 6IsSt.uniqueHyperreal.exists_st_of_not_infinite · cited by 4Hyperreal.exists_st_of_no…Hyperreal.IsSt.not_infinite · cited by 4IsSt.not_infiniteHyperreal.eq_of_isSt_real · cited by 3Hyperreal.eq_of_isSt_realHyperreal.IsSt.add · cited by 3IsSt.addHyperreal.IsSt.map₂ · cited by 3IsSt.map₂Hyperreal.IsSt.mul · cited by 3IsSt.mulHyperreal.isSt_iff · cited by 3Hyperreal.isSt_iffHyperreal.isSt_real_iff_eq · cited by 3Hyperreal.isSt_real_iff_eqHyperreal.st_eq · cited by 2Hyperreal.st_eqReal · cited by 25697RealHyperreal · cited by 172HyperrealHyperreal.ofReal · cited by 68Hyperreal.ofRealHyperreal.IsStCITED BYCITES

Cites3

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

Cited by44

Results whose statement or proof uses this declaration.