Theorems · Definition · functional analysis
CommCStarAlgebra.casesOn
{A : Type u_1} →
{motive : CommCStarAlgebra A → Sort u} →
(t : CommCStarAlgebra A) →
([toNormedCommRing : NormedCommRing A] →
[toStarRing : StarRing A] →
[toCompleteSpace : CompleteSpace A] →
[toCStarRing : CStarRing A] →
[toNormedAlgebra : NormedAlgebra ℂ A] →
[toStarModule : StarModule ℂ A] →
motive
{ toNormedCommRing := toNormedCommRing, toStarRing := toStarRing,
toCompleteSpace := toCompleteSpace, toCStarRing := toCStarRing,
toNormedAlgebra := toNormedAlgebra, toStarModule := toStarModule }) →
motive t- Defined in
- Mathlib.Analysis.CStarAlgebra.Classes
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- CompleteSpacestatement and proof · cited by 2,532
- StarRingstatement and proof · cited by 1,686
- NormedAlgebrastatement and proof · cited by 1,165
- StarModulestatement and proof · cited by 570
- NormedCommRingstatement and proof · cited by 218
- CStarRingstatement and proof · cited by 61
- CommCStarAlgebrastatement and proof · cited by 9
- Semiring.mul_zerostatement · cited by 3
- Semiring.zero_mulstatement · cited by 3
- Semiring.left_distribstatement · cited by 2
- Semiring.right_distribstatement · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- CommCStarAlgebra.noConfusionproof · cited by 0
- CommCStarAlgebra.noConfusionTypeproof · cited by 0