Theorems · Theorem · real analysis
Real.arcosh_cosh
∀ {x : ℝ}, 0 ≤ x → Real.arcosh (Real.cosh x) = xarcosh is the left inverse of cosh over $[0, ∞)$.
- Defined in
- Mathlib.Analysis.SpecialFunctions.Arcosh
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Real.expproof · cited by 871
- Real.sqrtproof · cited by 545
- Real.sinhproof · cited by 142
- Real.coshstatement and proof · cited by 119
- add_pos_of_pos_of_nonnegproof · cited by 63
- Real.exp_logproof · cited by 58
- Real.sq_sqrtproof · cited by 53
- Real.sqrt_nonnegproof · cited by 35
- sq_eq_sq₀proof · cited by 30
- Real.arcoshstatement · cited by 27
- eq_sub_iff_add_eq'proof · cited by 21
Cited by1
Results whose statement or proof uses this declaration.
- Real.coshPartialEquivproof · cited by 6