Theorems · Theorem · order theory
Submodule.add_mem_sup
∀ {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} {s t : M}, s ∈ S → t ∈ T → s + t ∈ S ⊔ T- Defined in
- Mathlib.Algebra.Module.Submodule.Lattice
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 65 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.
Cites7
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
- AddMemClass.add_memproof · cited by 229
- Submodule.mem_sup_rightproof · cited by 19
- Submodule.mem_sup_leftproof · cited by 14
Cited by6
Results whose statement or proof uses this declaration.
- Submodule.sup_smulproof · cited by 4
- LinearMap.range_add_leproof · cited by 2
- SchauderBasis.finrank_range_succSub_eq_oneproof · cited by 1
- Ideal.height_le_one_of_isPrincipal_of_mem_minimalPrimes_of_isLocalRingproof · cited by 1
- Submodule.sub_mem_supproof · cited by 0
- Submodule.map_add_leproof · cited by 0