Theorems · Theorem · real analysis
Real.cosh_arcosh
∀ {x : ℝ}, 1 ≤ x → Real.cosh (Real.arcosh x) = xarcosh is the right inverse of cosh over $[1, ∞)$.
- Defined in
- Mathlib.Analysis.SpecialFunctions.Arcosh
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Nat.cast_oneproof · cited by 2,501
- Real.logproof · cited by 939
- Real.expproof · cited by 871
- Real.sqrtproof · cited by 545
- lt_of_lt_of_leproof · cited by 438
- Real.coshstatement and proof · cited by 119
- add_pos_of_pos_of_nonnegproof · cited by 63
- Real.exp_logproof · cited by 58
- Real.sqrt_nonnegproof · cited by 35
- Real.exp_negproof · cited by 28
- Real.arcoshstatement · cited by 27
Cited by4
Results whose statement or proof uses this declaration.
- Real.coshPartialEquivproof · cited by 6
- Polynomial.Chebyshev.one_le_eval_T_realproof · cited by 2
- Polynomial.Chebyshev.one_lt_eval_T_realproof · cited by 2
- Real.tanh_arcoshproof · cited by 0