Theorems · Theorem · real analysis
Real.nat_sqrt_le_real_sqrt
∀ {a : ℕ}, ↑a.sqrt ≤ √↑aThe natural square root is at most the real square root
- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 132 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 · cited by 25,697
- Real.sqrtstatement · cited by 545
- Nat.cast_nonnegproof · cited by 109
- Real.le_sqrtproof · cited by 5
- Nat.sqrt_le'proof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- bertrand_main_inequalityproof · cited by 1
- Real.floor_real_sqrt_eq_nat_sqrtproof · cited by 0
- Real.nat_floor_real_sqrt_eq_nat_sqrtproof · cited by 0