Theorems · Theorem · functional analysis
norm_mul_eq_norm_left
∀ {E : Type u_5} [inst : SeminormedGroup E] (x : E) {y : E}, ‖y‖ = 0 → ‖x * y‖ = ‖x‖- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SeminormedGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- Norm.normstatement and proof · cited by 5,413
- add_zeroproof · cited by 2,707
- le_antisymmproof · cited by 2,068
- SeminormedGroupstatement and proof · cited by 250
- norm_mul_le'proof · cited by 15
- norm_le_mul_norm_addproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- norm_div_eq_norm_leftproof · cited by 1
- nnnorm_mul_eq_nnnorm_leftproof · cited by 0