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Theorems · Theorem · group theory

IsOfFinOrder.mono

∀ {G : Type u_1} {β : Type u_5} [inst : Monoid G] {x : G} [inst_1 : Monoid β] {y : β},
  IsOfFinOrder x → orderOf y ∣ orderOf x → IsOfFinOrder y
Defined in
Mathlib.GroupTheory.OrderOfElement
Cited by
2 results in Mathlib
Foundations
Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MonoidMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsOfFinOrder.fst · cited by 1IsOfFinOrder.fstIsOfFinOrder.snd · cited by 1IsOfFinOrder.sndMonoid · cited by 3887MonoidorderOf · cited by 324orderOfIsOfFinOrder · cited by 113IsOfFinOrderorderOf_pos_iff · cited by 8orderOf_pos_iffIsOfFinOrder.monoCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.