Theorems · Theorem · order theory
Submodule.mem_top
∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {x : M}, x ∈ ⊤- Defined in
- Mathlib.Algebra.Module.Submodule.Lattice
- Cited by
- 58 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses no axioms
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Top.topstatement · cited by 9,680
- Submodulestatement · cited by 7,192
Cited by59
Results whose statement or proof uses this declaration.
- Ideal.mul_topproof · cited by 42
- Submodule.topEquivproof · cited by 16
- AffineSubspace.direction_topproof · cited by 11
- Submodule.top_smulproof · cited by 11
- Module.le_comap_jacobsonproof · cited by 6
- Submodule.top_orthogonal_eq_botproof · cited by 6
- Ideal.radical_topproof · cited by 4
- Submodule.range_unitsToPicproof · cited by 4
- Ideal.IsTwoSided.mul_oneproof · cited by 3
- Submodule.span_smul_of_span_eq_topproof · cited by 3
- span_eq_top_of_isLocalizedModuleproof · cited by 3
- Ideal.eq_jacobson_iff_sInf_maximalproof · cited by 2