Theorems · Theorem · linear algebra

Submodule.map_strict_mono_or_ker_sup_lt_ker_sup

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

Defined in

Mathlib.LinearAlgebra.Span.Basic

Cited by

2 results in Mathlib

Foundations

Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingSemiringAddCommGroupModuleAddCommGroupModuleRingHomSurjective