Theorems · Theorem · linear algebra
Submodule.projection_apply_left
∀ {R : Type u_1} [inst : Ring R] {E : Type u_2} [inst_1 : AddCommGroup E] [inst_2 : Module R E] {p q : Submodule R E}
(hpq : IsCompl p q) (x : ↥p), (p.projection q hpq) ↑x = ↑x- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 73 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- IsComplstatement and proof · cited by 351
- Submodule.projectionstatement · cited by 63
- Submodule.projectionOnto_apply_leftproof · cited by 23
Cited by4
Results whose statement or proof uses this declaration.
- jacobson_densityproof · cited by 1
- Submodule.projectionL_apply_leftproof · cited by 0
- Submodule.projection_apply_of_mem_leftproof · cited by 0
- Submodule.IsCompl.projection_apply_leftproof · cited by 0