Theorems · Theorem · linear algebra
LinearMap.prod_eq_sup_map
∀ {R : Type u} {M : Type v} {M₂ : Type w} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : AddCommMonoid M₂]
[inst_3 : Module R M] [inst_4 : Module R M₂] (p : Submodule R M) (q : Submodule R M₂),
p.prod q = Submodule.map (LinearMap.inl R M M₂) p ⊔ Submodule.map (LinearMap.inr R M M₂) q- Defined in
- Mathlib.LinearAlgebra.Prod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 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
- Submodulestatement and proof · cited by 7,192
- Submodule.mapstatement and proof · cited by 614
- LinearMap.inlstatement and proof · cited by 72
- LinearMap.inrstatement and proof · cited by 62
- Submodule.prodstatement and proof · cited by 55
- Submodule.map_idproof · cited by 14
- LinearMap.coprod_inl_inrproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.span_inl_union_inrproof · cited by 2