Theorems · Theorem · group theory
exists_zsmul_surjective
∀ (G : Type u_2) [inst : SMul ℤ G] [IsAddCyclic G], ∃ g, Function.Surjective fun x => x • g
- Defined in
- Mathlib.Algebra.Group.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- SMulIsAddCyclic
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- IsAddCyclicstatement and proof · cited by 55
- IsAddCyclic.exists_zsmul_surjectiveproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- IsAddCyclic.exists_generatorproof · cited by 8
- not_isAddCyclic_of_denselyOrderedproof · cited by 1