Theorems · Theorem · real analysis
Real.cosh_arsinh
∀ (x : ℝ), Real.cosh (Real.arsinh x) = √(1 + x ^ 2)
- Defined in
- Mathlib.Analysis.SpecialFunctions.Arsinh
- Cited by
- 2 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.
Cites9
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
- LT.lt.leproof · cited by 2,189
- Real.sqrtstatement and proof · cited by 545
- Real.coshstatement · cited by 119
- Real.arsinhstatement and proof · cited by 55
- Real.sqrt_sqproof · cited by 36
- Real.sinh_arsinhproof · cited by 8
- Real.cosh_posproof · cited by 7
- Real.cosh_sq'proof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Real.hasStrictDerivAt_arsinhproof · cited by 3
- Real.tanh_arsinhproof · cited by 0