Theorems · Theorem · functional analysis
Dense.eq_zero_of_inner_right
∀ {E : Type u_4} (𝕜 : Type u_7) [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{x : E} {S : Set E}, Dense S → (∀ v ∈ S, inner 𝕜 v x = 0) → x = 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- map_zeroproof · cited by 1,614
- Inner.innerstatement and proof · cited by 1,089
- starRingEndproof · cited by 671
- Densestatement and proof · cited by 359
- inner_conj_symmproof · cited by 48
- Dense.eq_zero_of_inner_leftproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Dense.eq_of_inner_rightproof · cited by 2
- DenseRange.eq_zero_of_inner_rightproof · cited by 0
- LinearPMap.graph_adjoint_toLinearPMap_eq_adjointproof · cited by 0