Theorems · Theorem · linear algebra
LinearMap.iSup_range_single_le_iInf_ker_proj
∀ (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] (I J : Set ι),
Disjoint I J → ⨆ i ∈ I, (LinearMap.single R φ i).range ≤ ⨅ i ∈ J, (LinearMap.proj i).ker- Defined in
- Mathlib.LinearAlgebra.Pi
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapproof · cited by 10,215
- Top.topproof · cited by 9,680
- Submodulestatement · cited by 7,192
- iSupstatement · cited by 2,415
- Disjointstatement and proof · cited by 2,201
- iInfstatement and proof · cited by 1,690
Cited by2
Results whose statement or proof uses this declaration.
- LinearMap.iSup_range_single_eq_iInf_ker_projproof · cited by 2
- LinearMap.disjoint_single_singleproof · cited by 0