Theorems · Theorem · functional analysis
NormedSpace.Core.norm_eq_zero_iff
∀ {𝕜 : Type u_6} {E : Type u_7} [inst : NormedField 𝕜] [inst_1 : AddCommGroup E] [inst_2 : Module 𝕜 E]
[inst_3 : Norm E], NormedSpace.Core 𝕜 E → ∀ (x : E), ‖x‖ = 0 ↔ x = 0- Defined in
- Mathlib.Analysis.Normed.Module.Basic
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- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
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- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Norm.normstatement · cited by 5,413
- NormedFieldstatement and proof · cited by 1,084
- Normstatement and proof · cited by 512
- NormedSpace.Corestatement and proof · cited by 5
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