Theorems · Theorem · logic and foundations
Hyperreal.isSt_sSup
Deprecated since 2026-01-05Use ArchimedeanClass.stdPart_eq_sSup instead.
∀ {x : ℝ*}, ¬x.Infinite → x.IsSt (sSup {y | ↑y < x})- Defined in
- Mathlib.Analysis.Real.Hyperreal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Set.ofPredstatement · cited by 6,101
- SupSet.sSupstatement · cited by 954
- not_ltproof · cited by 306
- Hyperrealstatement and proof · cited by 172
- Hyperreal.ofRealstatement · cited by 68
- Hyperreal.Infinitestatement and proof · cited by 45
- Hyperreal.IsStstatement · cited by 42
- Hyperreal.coeRingHomproof · cited by 13
- Hyperreal.isSt_iffproof · cited by 3
- ArchimedeanClass.stdPart_eq_sSupproof · cited by 2
- Hyperreal.infinite_iffproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Hyperreal.isSt_st'proof · cited by 7
- Hyperreal.exists_st_of_not_infiniteproof · cited by 4