Theorems · Theorem · real analysis
Real.sq_sqrt
∀ {x : ℝ}, 0 ≤ x → √x ^ 2 = x- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 53 results in Mathlib
- Foundations
- Depth 128 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- sqproof · cited by 280
- Real.mul_self_sqrtproof · cited by 23
Cited by53
Results whose statement or proof uses this declaration.
- Real.log_sqrtproof · cited by 5
- CStarModule.norm_sq_eqproof · cited by 5
- LinearMap.sq_singularValues_finproof · cited by 4
- CFC.exists_sqrt_of_isSelfAdjoint_of_quasispectrumRestrictsproof · cited by 3
- OrthonormalBasis.sum_sq_norm_inner_rightproof · cited by 3
- Pell.exists_of_not_isSquareproof · cited by 3
- InnerProductSpace.volume_ball_of_dim_evenproof · cited by 3
- UpperHalfPlane.cosh_half_distproof · cited by 3
- CStarModule.norm_inner_leproof · cited by 2
- Real.add_sqrt_self_sq_sub_one_invproof · cited by 2
- integral_gaussianproof · cited by 2
- WithCStarModule.pi_norm_sqproof · cited by 2