Theorems · Theorem · linear algebra
LinearMap.IsProj.map_mem
∀ {S : Type u_5} [inst : Semiring S] {M : Type u_6} [inst_1 : AddCommMonoid M] [inst_2 : Module S M] {m : Submodule S M}
{F : Type u_7} [inst_3 : FunLike F M M] {f : F}, LinearMap.IsProj m f → ∀ (x : M), f x ∈ m- Defined in
- Mathlib.LinearAlgebra.Projection
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Submodulestatement and proof · cited by 7,192
- FunLikestatement and proof · cited by 2,560
- LinearMap.IsProjstatement and proof · cited by 23
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.IsProj.mem_iff_map_idproof · cited by 2
- LinearMap.isProj_iff_isIdempotentElemproof · cited by 1
- LinearMap.IsProj.submodule_eq_bot_iffproof · cited by 0