Theorems · Theorem · number theory
niven_sin
∀ {θ : ℝ}, (∃ r, θ = ↑r * Real.pi) → (∃ q, Real.sin θ = ↑q) → Real.sin θ ∈ {-1, -1 / 2, 0, 1 / 2, 1}Niven's theorem, but stated for sin instead of cos.
- Defined in
- Mathlib.NumberTheory.Niven
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- Real.cosproof · cited by 424
- Real.sinstatement and proof · cited by 389
- neg_eq_zeroproof · cited by 171
- sub_eq_zero_of_eqproof · cited by 154
- Rat.cast_oneproof · cited by 52
- Rat.cast_divproof · cited by 37
- Rat.cast_ofNatproof · cited by 19
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.