Theorems · Theorem · logic and foundations
Hyperreal.isSt_iff
Deprecated since 2026-01-05Mathlib marks this declaration as deprecated.
∀ {x : ℝ*} {r : ℝ}, x.IsSt r ↔ 0 ≤ ArchimedeanClass.mk x ∧ ArchimedeanClass.stdPart x = r- Defined in
- Mathlib.Analysis.Real.Hyperreal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 127 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- LT.lt.leproof · cited by 2,189
- zero_lt_oneproof · cited by 598
- ArchimedeanClassstatement · cited by 247
- add_sub_cancelproof · cited by 195
- ArchimedeanClass.mkstatement and proof · cited by 174
- Hyperrealstatement and proof · cited by 172
- sub_sub_cancelproof · cited by 105
- Hyperreal.ofRealproof · cited by 68
- ArchimedeanClass.stdPartstatement and proof · cited by 42
- Hyperreal.IsStstatement and proof · cited by 42
- sub_pos_of_ltproof · cited by 40
Cited by3
Results whose statement or proof uses this declaration.
- Hyperreal.st_eqproof · cited by 2
- Hyperreal.isSt_sSupproof · cited by 2
- Hyperreal.infinitesimal_iffproof · cited by 1