Theorems · Theorem · linear algebra
Submodule.factor_comp
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
{p p' p'' : Submodule R M} (H1 : p ≤ p') (H2 : p' ≤ p''),
Submodule.factor H2 ∘ₗ Submodule.factor H1 = Submodule.factor ⋯- Defined in
- Mathlib.LinearAlgebra.Quotient.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingAddCommGroupModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Submodulestatement and proof · cited by 7,192
- LE.le.transstatement and proof · cited by 3,151
- HasQuotient.Quotientstatement · cited by 2,301
- LinearMap.compstatement · cited by 1,642
- LinearMap.extproof · cited by 844
- Submodule.Quotient.mkproof · cited by 184
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.factor_comp_applyproof · cited by 2