Theorems · Theorem · real analysis
Real.sin_eq_zero_iff
∀ {x : ℝ}, Real.sin x = 0 ↔ ∃ n, ↑n * Real.pi = x- Cited by
- 5 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- add_zeroproof · cited by 2,707
- MulZeroClass.mul_zeroproof · cited by 2,091
- le_antisymmproof · cited by 2,068
- Real.pistatement and proof · cited by 1,774
- MulZeroClass.zero_mulproof · cited by 1,625
- sub_eq_add_negproof · cited by 1,023
- LT.lt.neproof · cited by 872
- neg_zeroproof · cited by 542
- le_of_not_gtproof · cited by 430
- Real.cosproof · cited by 424
- Real.sinstatement and proof · cited by 389
Cited by5
Results whose statement or proof uses this declaration.
- Real.Angle.cos_eq_iff_coe_eq_or_eq_negproof · cited by 3
- Polynomial.Chebyshev.roots_U_realproof · cited by 2
- Real.cos_eq_one_iffproof · cited by 2
- Real.quadratic_root_cos_pi_div_fiveproof · cited by 2
- Real.sin_ne_zero_iffproof · cited by 0