Theorems · Theorem · group theory
IsOfFinOrder.apply
∀ {η : Type u_6} {Gs : η → Type u_7} [inst : (i : η) → Monoid (Gs i)] {x : (i : η) → Gs i},
IsOfFinOrder x → ∀ (i : η), IsOfFinOrder (x i)If a direct product has finite order then so does each component.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- IsOfFinOrderstatement and proof · cited by 113
- isOfFinOrder_iff_pow_eq_oneproof · cited by 27
- IsOfFinOrder.exists_pow_eq_oneproof · cited by 4
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.