Theorems · Theorem · commutative algebra
Submodule.nonempty
∀ {R : Type u} {M : Type v} [inst : Semiring R] [inst_1 : AddCommMonoid M] {module_M : Module R M} (p : Submodule R M),
(↑p).Nonempty- Defined in
- Mathlib.Algebra.Module.Submodule.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses no axioms
- Assumes
- SemiringAddCommMonoid
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
- SetLike.coestatement · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.Nonemptystatement · cited by 2,627
- Submodule.zero_memproof · cited by 58
Cited by3
Results whose statement or proof uses this declaration.
- Submodule.isPathConnectedproof · cited by 1
- ProperCone.nonemptyproof · cited by 0
- ZLattice.comap_span_topproof · cited by 0