Theorems · Theorem · order theory
Submodule.mem_sup_right
∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
{S T : Submodule R M} {x : M}, x ∈ T → x ∈ S ⊔ T- Defined in
- Mathlib.Algebra.Module.Submodule.Lattice
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- 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
- Submodulestatement and proof · cited by 7,192
- le_sup_rightproof · cited by 242
Cited by19
Results whose statement or proof uses this declaration.
- Ideal.radical_eq_sInfproof · cited by 21
- Submodule.add_mem_supproof · cited by 6
- HahnEmbedding.ArchimedeanStrata.archimedeanClassMk_of_mem_stratumproof · cited by 3
- LieAlgebra.IsKilling.sl2SubmoduleOfRoot_eq_supproof · cited by 3
- TensorProduct.exists_finite_submodule_of_setFiniteproof · cited by 3
- LinearPMap.supSpanSingleton_apply_selfstatement and proof · cited by 2
- TensorProduct.Algebra.eq_of_fg_of_subtype_eqproof · cited by 2
- HahnEmbedding.Partial.lt_extendproof · cited by 1
- LinearPMap.supSpanSingleton_apply_smul_selfstatement · cited by 1
- Ideal.finrank_quotient_mapproof · cited by 1
- HahnEmbedding.Partial.truncLT_eval_mem_range_extendFunproof · cited by 1
- LieSubalgebra.lie_mem_sup_of_mem_normalizerproof · cited by 1