Theorems · Theorem · functional analysis
InnerProductSpace.Core.inner_self_ne_zero
∀ {𝕜 : Type u_1} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : AddCommGroup F] [inst_2 : Module 𝕜 F]
[cd : InnerProductSpace.Core 𝕜 F] {x : F}, inner 𝕜 x x ≠ 0 ↔ x ≠ 0- Defined in
- Mathlib.Analysis.InnerProductSpace.Defs
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- 0 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Quot.sound
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- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- RCLikestatement and proof · cited by 2,829
- Inner.innerstatement · cited by 1,089
- Iff.notproof · cited by 489
- InnerProductSpace.Corestatement and proof · cited by 10
- InnerProductSpace.Core.toInner'statement · cited by 2
- InnerProductSpace.Core.inner_self_eq_zeroproof · cited by 2
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