Theorems · Theorem · linear algebra
Submodule.baseChange_mono
∀ {R : Type u_1} {M : Type u_2} (A : Type u_3) [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A]
[inst_3 : AddCommMonoid M] [inst_4 : Module R M] {p q : Submodule R M},
p ≤ q → Submodule.baseChange A p ≤ Submodule.baseChange A q- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- RingHom.idproof · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapproof · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- TensorProductstatement and proof · cited by 2,545
- LinearMap.compproof · cited by 1,642
- LinearMap.rangeproof · cited by 893
- LinearMap.idproof · cited by 625
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.baseChange_le_iffproof · cited by 0