Theorems · Theorem · number theory
niven_fract_angle_div_pi_eq
∀ {r : ℚ}, (∃ q, Real.cos (↑r * Real.pi) = ↑q) → Int.fract r ∈ {0, 1 / 3, 1 / 2, 2 / 3}- Defined in
- Mathlib.NumberTheory.Niven
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Real.pistatement and proof · cited by 1,774
- le_of_ltproof · cited by 1,175
- Real.cosstatement and proof · cited by 424
- Int.floorproof · cited by 225
- sub_mulproof · cited by 170
- Int.fractstatement and proof · cited by 114
- Rat.cast_intCastproof · cited by 74
- Rat.cast_oneproof · cited by 52
- Rat.cast_negproof · cited by 25
- Int.fract_lt_oneproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- irrational_cos_rat_mul_piproof · cited by 1