Theorems · Theorem · real analysis
Real.add_sqrt_self_sq_sub_one_inv
∀ {x : ℝ}, 1 ≤ x → (x + √(x ^ 2 - 1))⁻¹ = x - √(x ^ 2 - 1)- Defined in
- Mathlib.Analysis.SpecialFunctions.Arcosh
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 129 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.sqrtstatement and proof · cited by 545
- sub_sub_cancelproof · cited by 105
- Real.sq_sqrtproof · cited by 53
- sub_nonneg_of_leproof · cited by 37
- one_le_pow₀proof · cited by 25
- inv_eq_of_mul_eq_one_rightproof · cited by 15
- pow_two_sub_pow_twoproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Real.cosh_arcoshproof · cited by 3
- Real.sinh_arcoshproof · cited by 2