Theorems · Theorem · linear algebra
Submodule.comap_sup_of_injective
∀ {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]
{f : M →ₛₗ[σ₁₂] M₂} [inst_6 : RingHomSurjective σ₁₂] {p q : Submodule R₂ M₂},
Function.Injective ⇑f →
p ≤ f.range → q ≤ f.range → Submodule.comap f (p ⊔ q) = Submodule.comap f p ⊔ Submodule.comap f q- Defined in
- Mathlib.LinearAlgebra.Span.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement and proof · cited by 10,215
- RingHomstatement and proof · cited by 10,189
- Submodulestatement and proof · cited by 7,192
- LinearMap.rangestatement and proof · cited by 893
- Submodule.mapproof · cited by 614
- Submodule.comapstatement and proof · cited by 347
- RingHomSurjectivestatement and proof · cited by 220
- Submodule.map_injective_of_injectiveproof · cited by 31
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.Generators.exists_presentation_of_basis_cotangentproof · cited by 2