Theorems · Theorem · real analysis
Real.sqrt_pos
∀ {x : ℝ}, 0 < √x ↔ 0 < x- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 16 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.
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
- lt_iff_lt_of_le_iff_leproof · cited by 54
- Real.sqrt_eq_zero'proof · cited by 3
Cited by16
Results whose statement or proof uses this declaration.
- Real.sqrt_pos_of_posproof · cited by 50
- Behrend.nValue_posproof · cited by 3
- Real.deriv_sqrt_auxproof · cited by 2
- Real.deriv_arcsin_auxproof · cited by 2
- InnerProductGeometry.angle_add_lt_pi_div_two_of_inner_eq_zeroproof · cited by 2
- InnerProductGeometry.angle_add_pos_of_inner_eq_zeroproof · cited by 2
- Behrend.dValue_posproof · cited by 1
- Behrend.lower_bound_le_one'proof · cited by 1
- Behrend.roth_lower_bound_explicitproof · cited by 1
- strictConcaveOn_sqrt_mul_log_Ioiproof · cited by 1
- isConformalMap_iffproof · cited by 1
- Real.sqrt_le_sqrt_iff'proof · cited by 1