Theorems · Theorem · linear algebra
Submodule.sup_toAddSubmonoid
∀ {R : Type u_1} {M : Type u_4} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
(p p' : Submodule R M), (p ⊔ p').toAddSubmonoid = p.toAddSubmonoid ⊔ p'.toAddSubmonoid- Defined in
- Mathlib.LinearAlgebra.Span.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 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.
Cites10
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
- AddSubmonoidstatement · cited by 1,178
- Submodule.toAddSubmonoidstatement and proof · cited by 162
- Submodule.mem_supproof · cited by 73
- AddSubmonoid.extproof · cited by 32
- AddSubmonoid.mem_supproof · cited by 8
- Submodule.mem_toAddSubmonoidproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.smul_supproof · cited by 3