Theorems · Theorem · linear algebra
Submodule.subtype_injective
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] {module_M : Module R M} (p : Submodule R M),
Function.Injective ⇑p.subtype- Cited by
- 25 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- SemiringAddCommMonoid
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 · 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
- Submodule.subtypestatement · cited by 480
- Subtype.coe_injectiveproof · cited by 205
Cited by25
Results whose statement or proof uses this declaration.
- linearIndependent_iff_card_eq_finrank_spanproof · cited by 5
- IsSemisimpleModule.eq_bot_or_exists_simple_leproof · cited by 4
- isIsotypicOfType_submodule_iffproof · cited by 4
- Submodule.spanRank_topproof · cited by 3
- isFullyInvariant_iff_le_imp_isotypicComponent_leproof · cited by 2
- ZLattice.exists_forall_abs_repr_le_normproof · cited by 2
- Submodule.le_linearEquiv_of_le_sSupproof · cited by 2
- Submodule.le_linearEquiv_of_sSup_eq_topproof · cited by 2
- Algebra.Generators.exists_presentation_of_basis_cotangentproof · cited by 2
- Module.length_le_of_surjectiveproof · cited by 2
- Submodule.powSMulQuotInclusion_injectiveproof · cited by 1
- LinearMap.ker_inf_smul_top_eq_smul_of_flatproof · cited by 1