Theorems · Theorem · linear algebra

LinearMap.coprodEquiv_apply

∀ {R : Type u} {M : Type v} {M₂ : Type w} {M₃ : Type y} (S : Type u_3) [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : AddCommMonoid M₃] [inst_5 : Module R M]
  [inst_6 : Module R M₂] [inst_7 : Module R M₃] [inst_8 : Module S M₃] [inst_9 : SMulCommClass R S M₃]
  (f : (M →ₗ[R] M₃) × (M₂ →ₗ[R] M₃)), (LinearMap.coprodEquiv S) f = f.1.coprod f.2

Defined in: Mathlib.LinearAlgebra.Prod
Cited by: 1 results in Mathlib
Foundations: Depth 34 from the axioms · uses propext, Quot.sound
Assumes: Semiring Semiring AddCommMonoid AddCommMonoid AddCommMonoid Module Module Module Module SMulCommClass

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Cites10

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
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
LinearEquivstatement · cited by 3,317
SMulCommClassstatement and proof · cited by 1,927
LinearMap.coprodstatement · cited by 38
LinearMap.coprodEquivstatement and proof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

IsLocalExtrOn.exists_linear_map_of_hasStrictFDerivAtproof · cited by 2