Theorems · Theorem · linear algebra
LinearMap.coprod_inl_inr
∀ {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], (LinearMap.inl R M M₂).coprod (LinearMap.inr R M M₂) = LinearMap.id- Defined in
- Mathlib.LinearAlgebra.Prod
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- LinearMap.extproof · cited by 844
- LinearMap.idstatement · cited by 625
- LinearMap.inlstatement · cited by 72
- LinearMap.inrstatement · cited by 62
- LinearMap.coprodstatement · cited by 38
Cited by4
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.coprod_inl_inrproof · cited by 2
- LinearMap.prod_eq_sup_mapproof · cited by 1
- Representation.IntertwiningMap.coprod_inl_inrproof · cited by 0
- LinearMap.coprod_comp_inl_inrproof · cited by 0