Theorems · Theorem · logic and foundations
Hyperreal.infinitePos_iff_infinite_of_nonneg
Deprecated since 2026-01-05Mathlib marks this declaration as deprecated.
∀ {x : ℝ*}, 0 ≤ x → (x.InfinitePos ↔ x.Infinite)- Defined in
- Mathlib.Analysis.Real.Hyperreal
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.not_geproof · cited by 305
- Hyperrealstatement and proof · cited by 172
- Hyperreal.Infinitestatement · cited by 45
- Hyperreal.InfinitePosstatement · cited by 44
- Hyperreal.InfiniteNegproof · cited by 38
- Hyperreal.InfiniteNeg.lt_zeroproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Hyperreal.infinitePos_abs_iff_infinite_absproof · cited by 1
- Hyperreal.infinitePos_iff_infinite_of_posproof · cited by 0