Theorems · Theorem · real analysis
Real.nat_floor_real_sqrt_eq_nat_sqrt
∀ {a : ℕ}, ⌊√↑a⌋₊ = a.sqrtThe natural floor of the real square root is the same as the natural square root.
- Defined in
- Mathlib.Analysis.Real.Sqrt
- Cited by
- 0 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.
Cites7
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.floorstatement · cited by 215
- Real.sqrt_nonnegproof · cited by 35
- Nat.floor_eq_iffproof · cited by 5
- Real.real_sqrt_lt_nat_sqrt_succproof · cited by 3
- Real.nat_sqrt_le_real_sqrtproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.