Theorems · Theorem · linear algebra

Submodule.span_image

∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_4} {M₂ : Type u_5} [inst : Semiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] [inst_3 : Semiring R₂] {σ₁₂ : R →+* R₂} [inst_4 : AddCommMonoid M₂] [inst_5 : Module R₂ M₂]
  {s : Set M} [inst_6 : RingHomSurjective σ₁₂] (f : M →ₛₗ[σ₁₂] M₂),
  Submodule.span R₂ (⇑f '' s) = Submodule.map f (Submodule.span R s)

Defined in

Mathlib.LinearAlgebra.Span.Basic

Cited by

25 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleSemiringAddCommMonoidModuleRingHomSurjective