Theorems · Theorem · functional analysis
ClosedSubmodule.symplComp_symplComp_eq
∀ {H : Type u_1} [inst : NormedAddCommGroup H] [ipc : InnerProductSpace ℂ H] [CompleteSpace H]
{S : ClosedSubmodule ℝ H}, S.symplComp.symplComp = S- Cited by
- 1 results in Mathlib
- Foundations
- Depth 186 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.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Complexstatement and proof · cited by 5,565
- InnerProductSpacestatement and proof · cited by 3,523
- CompleteSpacestatement and proof · cited by 2,532
- ClosedSubmodulestatement and proof · cited by 123
- ClosedSubmodule.orthogonalproof · cited by 32
- ClosedSubmodule.symplCompstatement · cited by 7
- ClosedSubmodule.orthogonal_orthogonal_eqproof · cited by 3
- ClosedSubmodule.mulI_mulI_eqproof · cited by 2
- ClosedSubmodule.mulI_symplCompproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- StandardSubspace.symplComp_symplComp_eqproof · cited by 1