Theorems · Theorem · functional analysis
InnerProductSpace.Core.inner_self_ofReal_re
∀ {𝕜 : Type u_1} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : AddCommGroup F] [inst_2 : Module 𝕜 F]
[c : PreInnerProductSpace.Core 𝕜 F] (x : F), ↑(RCLike.re (inner 𝕜 x x)) = inner 𝕜 x x- Defined in
- Mathlib.Analysis.InnerProductSpace.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- Inner.innerstatement and proof · cited by 1,089
- RCLike.ofRealstatement and proof · cited by 350
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement and proof · cited by 319
- RCLike.ofReal_reproof · cited by 60
- PreInnerProductSpace.Corestatement and proof · cited by 46
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