Theorems · Theorem · real analysis
Real.exp_arsinh
∀ (x : ℝ), Real.exp (Real.arsinh x) = x + √(1 + x ^ 2)
- Defined in
- Mathlib.Analysis.SpecialFunctions.Arsinh
- Cited by
- 2 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.
Cites8
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.expstatement · cited by 871
- Real.sqrtstatement · cited by 545
- Even.neg_powproof · cited by 99
- Real.exp_logproof · cited by 58
- Real.arsinhstatement · cited by 55
- neg_lt_iff_pos_add'proof · cited by 6
- Real.lt_sqrt_of_sq_ltproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- Real.sinh_arsinhproof · cited by 8
- Real.arsinh_negproof · cited by 1