Theorems · Theorem · logic and foundations
Hyperreal.infinite_abs_iff
Deprecated since 2026-01-05Mathlib marks this declaration as deprecated.
∀ {x : ℝ*}, |x|.Infinite ↔ x.Infinite- Defined in
- Mathlib.Analysis.Real.Hyperreal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 119 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.
- absstatement · cited by 1,814
- le_totalproof · cited by 294
- abs_of_nonnegproof · cited by 279
- Hyperrealstatement and proof · cited by 172
- abs_of_nonposproof · cited by 53
- Hyperreal.Infinitestatement and proof · cited by 45
Cited by1
Results whose statement or proof uses this declaration.
- Hyperreal.infinitePos_abs_iff_infiniteproof · cited by 1