Theorems · Theorem · number theory
irrational_cos_rat_mul_pi
∀ {r : ℚ}, 3 < r.den → Irrational (Real.cos (↑r * Real.pi))- Defined in
- Mathlib.NumberTheory.Niven
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Real.pistatement and proof · cited by 1,774
- Real.cosstatement and proof · cited by 424
- Set.mem_singleton_iffproof · cited by 172
- Irrationalstatement and proof · cited by 139
- Int.fractproof · cited by 114
- Rat.den_intFractproof · cited by 1
- niven_fract_angle_div_pi_eqproof · cited by 1
- exists_rat_of_not_irrationalproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.irrational_of_isRoot_T_realproof · cited by 0