Theorems · Theorem · linear algebra
LinearMap.iSup_range_single
∀ (R : Type u) {ι : Type x} [inst : Semiring R] (φ : ι → Type i) [inst_1 : (i : ι) → AddCommMonoid (φ i)]
[inst_2 : (i : ι) → Module R (φ i)] [inst_3 : DecidableEq ι] [Finite ι], ⨆ i, (LinearMap.single R φ i).range = ⊤- Defined in
- Mathlib.LinearAlgebra.Pi
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
- Finitestatement and proof · cited by 3,029
- iSupstatement and proof · cited by 2,415
- iInfproof · cited by 1,690
- LinearMap.rangestatement and proof · cited by 893
- LinearMap.kerproof · cited by 848
- iSup_congr_Propproof · cited by 247
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.range_diagonalproof · cited by 1