Theorems · Theorem · real analysis
Real.artanh_le_artanh_iff
∀ {x y : ℝ}, x ∈ Set.Ioo (-1) 1 → y ∈ Set.Ioo (-1) 1 → (Real.artanh x ≤ Real.artanh y ↔ x ≤ y)- Defined in
- Mathlib.Analysis.SpecialFunctions.Artanh
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 175 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.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.Ioostatement and proof · cited by 1,214
- Real.artanhstatement · cited by 20
- StrictMonoOn.le_iff_leproof · cited by 17
- Real.strictMonoOn_artanhproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Real.artanh_le_artanhproof · cited by 0
- Real.artanh_nonnegproof · cited by 0
- Real.artanh_nonposproof · cited by 0