Theorems · Theorem · real analysis
Real.cos_sub_int_mul_pi
∀ (x : ℝ) (n : ℤ), Real.cos (x - ↑n * Real.pi) = (-1) ^ n * Real.cos x
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Real.pistatement · cited by 1,774
- Real.cosstatement · cited by 424
- Real.cos_antiperiodicproof · cited by 16
- Int.cast_negOnePowproof · cited by 10
- Function.Antiperiodic.sub_int_mul_eqproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- niven_fract_angle_div_pi_eqproof · cited by 1