Theorems · Theorem · functional analysis
norm_div_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
- 1 results in Mathlib
- Foundations
- Depth 102 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.
Cites6
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
- Norm.normstatement and proof · cited by 5,413
- div_eq_mul_invproof · cited by 715
- SeminormedGroupstatement and proof · cited by 250
- norm_inv'proof · cited by 23
- norm_mul_eq_norm_leftproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- nnnorm_div_eq_nnnorm_leftproof · cited by 0