Theorems · Theorem · linear algebra
LinearMap.coprod_comp_inl_inr
∀ {R : Type u} {M : Type v} {M₂ : Type w} {M₃ : Type y} [inst : Semiring R] [inst_1 : AddCommMonoid M]
[inst_2 : AddCommMonoid M₂] [inst_3 : AddCommMonoid M₃] [inst_4 : Module R M] [inst_5 : Module R M₂]
[inst_6 : Module R M₃] (f : M × M₂ →ₗ[R] M₃), (f ∘ₗ LinearMap.inl R M M₂).coprod (f ∘ₗ LinearMap.inr R M M₂) = f- Defined in
- Mathlib.LinearAlgebra.Prod
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
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Cites12
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- 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
- LinearMapstatement and proof · cited by 10,215
- LinearMap.compstatement and proof · cited by 1,642
- LinearMap.inlstatement and proof · cited by 72
- LinearMap.inrstatement and proof · cited by 62
- LinearMap.coprodstatement · cited by 38
- LinearMap.comp_idproof · cited by 17
- LinearMap.coprod_inl_inrproof · cited by 4
- LinearMap.comp_coprodproof · cited by 2
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