Theorems · Theorem · functional analysis
norm_div_pos_iff
∀ {E : Type u_5} [inst : NormedGroup E] {a b : E}, 0 < ‖a / b‖ ↔ a ≠ b- Defined in
- Mathlib.Analysis.Normed.Group.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedGroup
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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 · cited by 5,413
- Iff.notproof · cited by 489
- LE.le.lt_iff_neproof · cited by 34
- norm_nonneg'proof · cited by 21
- NormedGroupstatement and proof · cited by 18
- norm_div_eq_zero_iffproof · cited by 2
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