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Theorems · Theorem · functional analysis

SameRay.norm_smul_eq

∀ {E : Type u_1} [inst : SeminormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] {x y : E},
  SameRay ℝ x y → ‖x‖ • y = ‖y‖ • x
Defined in
Mathlib.Analysis.Normed.Module.Ray
Cited by
1 results in Mathlib
Foundations
Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
SeminormedAddCommGroupNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

sameRay_iff_norm_smul_eq · cited by 1sameRay_iff_norm_smul_eqReal · cited by 25697RealNormedSpace · cited by 12499NormedSpaceNorm.norm · cited by 5413Norm.normSeminormedAddCommGroup · cited by 2671SeminormedAddCommGroupSemigroupAction.mul_smul · cited by 291SemigroupAction.mul_smulSameRay · cited by 149SameRaySMulCommClass.smul_comm · cited by 143SMulCommClass.smul_commnorm_smul_of_nonneg · cited by 7norm_smul_of_nonnegSameRay.exists_eq_smul · cited by 3SameRay.exists_eq_smulSameRay.norm_smul_eqCITED BYCITES

Cites9

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Cited by1

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