Theorems · Theorem · functional analysis
InnerProductSpace.Core.inner_neg_left
∀ {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 y : F), inner 𝕜 (-x) y = -inner 𝕜 x y- Defined in
- Mathlib.Analysis.InnerProductSpace.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- one_mulproof · cited by 2,841
- RCLikestatement and proof · cited by 2,829
- Inner.innerstatement and proof · cited by 1,089
- map_oneproof · cited by 861
- starRingEndproof · cited by 671
- neg_mulproof · cited by 654
- map_negproof · cited by 378
- PreInnerProductSpace.Corestatement and proof · cited by 46
- InnerProductSpace.Core.toPreInner'statement · cited by 32
- neg_one_smulproof · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- InnerProductSpace.Core.inner_neg_rightproof · cited by 1
- InnerProductSpace.Core.inner_sub_leftproof · cited by 1