Theorems · Theorem · Lie groups
Circle.norm_smul
∀ {E : Type u_4} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] (u : Circle) (v : E), ‖u • v‖ = ‖v‖- Defined in
- Mathlib.Analysis.Complex.Circle
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- Norm.normstatement and proof · cited by 5,413
- one_mulproof · cited by 2,841
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- norm_smulproof · cited by 242
- Circlestatement and proof · cited by 227
- norm_eq_of_mem_sphereproof · cited by 11
- Circle.smul_defproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- VectorFourier.fourierIntegral_convergent_iffproof · cited by 9
- VectorFourier.hasFDerivAt_fourierIntegralproof · cited by 5
- VectorFourier.norm_fourierIntegral_le_integral_normproof · cited by 4
- SchwartzMap.norm_fourier_apply_le_toLp_oneproof · cited by 2
- VectorFourier.integral_fourierIntegral_swapproof · cited by 2
- Real.fourier_bilin_convolution_eq_integralproof · cited by 1
- VectorFourier.fourierIntegral_continuousproof · cited by 1
- tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_supportproof · cited by 1