Theorems · Theorem · real analysis
Real.le_sqrt_of_sq_le
∀ {x y : ℝ}, x ^ 2 ≤ y → x ≤ √y- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 133 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- LE.le.transproof · cited by 3,151
- Real.sqrtstatement · cited by 545
- sq_nonnegproof · cited by 106
- Real.sq_leproof · cited by 2
Cited by10
Results whose statement or proof uses this declaration.
- Real.pi_lower_bound_startproof · cited by 5
- Real.sqrtTwoAddSeries_step_downproof · cited by 5
- Complex.norm_sub_mem_Icc_angleproof · cited by 2
- one_add_norm_le_sqrt_two_mul_sqrtproof · cited by 1
- Real.sum_mul_le_sqrt_mul_sqrtproof · cited by 1
- Behrend.dValue_posproof · cited by 1
- Behrend.le_sqrt_logproof · cited by 1
- Behrend.log_two_mul_two_le_sqrt_log_eightproof · cited by 1
- Behrend.boundproof · cited by 1
- UpperHalfPlane.isProperMap_smul_Iproof · cited by 0