Theorems · Theorem · linear algebra
Submodule.inclusion_injective
∀ {R : Type u_1} {M : Type u_2} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{p p' : Submodule R M} (h : p ≤ p'), Function.Injective ⇑(Submodule.inclusion h)- Cited by
- 15 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- Submodulestatement and proof · cited by 7,192
- Subtype.val_injectiveproof · cited by 232
- Submodule.inclusionstatement and proof · cited by 74
Cited by15
Results whose statement or proof uses this declaration.
- Submodule.LinearDisjoint.of_le_left_of_flatproof · cited by 4
- Submodule.LinearDisjoint.of_le_right_of_flatproof · cited by 4
- le_isotypicComponent_iffproof · cited by 2
- Subalgebra.finrank_sup_le_of_freeproof · cited by 2
- Submodule.le_linearEquiv_of_le_sSupproof · cited by 2
- LieModule.isNilpotent_of_leproof · cited by 1
- Submodule.isAtom_iff_finrank_eq_oneproof · cited by 1
- CovBy.length_baseChangeproof · cited by 1
- CovBy.length_restrictScalarsproof · cited by 1
- Subalgebra.LinearDisjoint.of_finrank_coprime_of_freeproof · cited by 1
- isArtinian_of_leproof · cited by 0
- sSupIndep_isotypicComponentsproof · cited by 0