Theorems · Theorem · Lie groups
Circle.coe_exp
∀ (t : ℝ), ↑(Circle.exp t) = Complex.exp (↑t * Complex.I)
- Defined in
- Mathlib.Analysis.Complex.Circle
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realstatement and proof · cited by 25,697
- Complexstatement · cited by 5,565
- Submonoidstatement · cited by 3,086
- ContinuousMapstatement · cited by 2,491
- Complex.ofRealstatement · cited by 1,654
- Complex.Istatement · cited by 866
- Complex.expstatement · cited by 612
- Circlestatement · cited by 227
- Submonoid.unitSpherestatement · cited by 85
- Circle.expstatement · cited by 73
Cited by10
Results whose statement or proof uses this declaration.
- fourier_coe_applyproof · cited by 7
- Circle.exp_zeroproof · cited by 5
- Circle.arg_expproof · cited by 3
- Circle.exp_pi_ne_oneproof · cited by 2
- ZMod.toCircle_intCastproof · cited by 2
- Real.Angle.arg_toCircleproof · cited by 2
- Circle.exp_eq_expproof · cited by 2
- fourier_add_half_inv_indexproof · cited by 1
- ZMod.toCircle_eq_circleExpproof · cited by 0
- argSelfAdjoint_expUnitaryproof · cited by 0