Theorems · Theorem · real analysis
Complex.cos_int_mul_two_pi_sub_pi
∀ (n : ℤ), Complex.cos (↑n * (2 * ↑Real.pi) - ↑Real.pi) = -1
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- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement · cited by 5,565
- Real.pistatement and proof · cited by 1,774
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.cosstatement and proof · cited by 279
- Function.Periodic.int_mulproof · cited by 18
- Complex.cos_periodicproof · cited by 15
- Complex.cos_zeroproof · cited by 14
- Complex.cos_antiperiodicproof · cited by 9
- Function.Periodic.sub_antiperiod_eqproof · cited by 4
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