Theorems · Theorem · linear algebra

LinearMap.map_le_map_iff

∀ {R : Type u_1} {R₂ : Type u_2} {M : Type u_4} {M₂ : Type u_5} [inst : Semiring R] [inst_1 : Semiring R₂]
  [inst_2 : AddCommGroup M] [inst_3 : AddCommGroup M₂] [inst_4 : Module R M] [inst_5 : Module R₂ M₂] {τ₁₂ : R →+* R₂}
  [inst_6 : RingHomSurjective τ₁₂] (f : M →ₛₗ[τ₁₂] M₂) {p p' : Submodule R M},
  Submodule.map f p ≤ Submodule.map f p' ↔ p ≤ p' ⊔ f.ker

Defined in

Mathlib.LinearAlgebra.Span.Basic

Cited by

2 results in Mathlib

Foundations

Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommGroupAddCommGroupModuleModuleRingHomSurjective