Theorems · Theorem · functional analysis
norm_div_eq_zero_iff
∀ {E : Type u_5} [inst : NormedGroup E] {a b : E}, ‖a / b‖ = 0 ↔ a = b- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 5,413
- NormedGroupstatement and proof · cited by 18
- div_eq_oneproof · cited by 11
- norm_eq_zero'proof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- eq_of_norm_div_eq_zeroproof · cited by 0
- norm_div_pos_iffproof · cited by 0