Theorems · Theorem · linear algebra
LinearMap.isCompl_of_proj
∀ {R : Type u_1} [inst : Ring R] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module R E] {p : Submodule R E}
{f : E →ₗ[R] ↥p}, (∀ (x : ↥p), f ↑x = x) → IsCompl p f.ker- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement and proof · cited by 10,215
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- Bot.botproof · cited by 4,720
- sub_selfproof · cited by 996
- LinearMap.kerstatement and proof · cited by 848
Cited by5
Results whose statement or proof uses this declaration.
- Submodule.exists_isComplproof · cited by 7
- LinearMap.IsProj.isComplproof · cited by 6
- LinearMap.projectionOnto_of_projstatement and proof · cited by 1
- MonoidAlgebra.Submodule.exists_isComplproof · cited by 0
- LinearMap.linearProjOfIsCompl_of_projstatement · cited by 0