Theorems · Theorem · logic and foundations
Hyperreal.infinitePos_iff
Deprecated since 2026-01-05Mathlib marks this declaration as deprecated.
∀ {x : ℝ*}, x.InfinitePos ↔ 0 < x ∧ ArchimedeanClass.mk x < 0- Defined in
- Mathlib.Analysis.Real.Hyperreal
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- mul_oneproof · cited by 3,885
- LT.lt.leproof · cited by 2,189
- LT.lt.trans_leproof · cited by 678
- nsmul_eq_mulproof · cited by 369
- ArchimedeanClassstatement · cited by 247
- ArchimedeanClass.mkstatement and proof · cited by 174
- Hyperrealstatement and proof · cited by 172
- abs_of_posproof · cited by 114
- abs_oneproof · cited by 87
- Hyperreal.ofRealproof · cited by 68
- Hyperreal.InfinitePosstatement and proof · cited by 44
Cited by3
Results whose statement or proof uses this declaration.
- Hyperreal.infinitePos_iff_infinitesimal_inv_posproof · cited by 5
- Hyperreal.infinite_iffproof · cited by 1
- Hyperreal.infinitePos_of_tendsto_topproof · cited by 0