Theorems · Theorem · logic and foundations
Hyperreal.infinitesimal_inv_of_infinite
Deprecated since 2026-01-05Mathlib marks this declaration as deprecated.
∀ {x : ℝ*}, x.Infinite → x⁻¹.Infinitesimal- Defined in
- Mathlib.Analysis.Real.Hyperreal
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 131 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Hyperrealstatement and proof · cited by 172
- Hyperreal.Infinitestatement and proof · cited by 45
- Hyperreal.InfinitePosproof · cited by 44
- Hyperreal.Infinitesimalstatement · cited by 41
- Hyperreal.InfiniteNegproof · cited by 38
- Hyperreal.infinitePos_iff_infinitesimal_inv_posproof · cited by 5
- Hyperreal.infiniteNeg_iff_infinitesimal_inv_negproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- Hyperreal.infinite_iff_infinitesimal_invproof · cited by 2