Theorems · Theorem · group theory
MulEquiv.orderOf_eq
∀ {G : Type u_1} [inst : Monoid G] {H : Type u_6} [inst_1 : Monoid H] (e : G ≃* H) (x : G), orderOf (e x) = orderOf xA multiplicative equivalence preserves orders of elements.
- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement · cited by 62,936
- Monoidstatement and proof · cited by 3,887
- MulEquivstatement and proof · cited by 1,142
- orderOfstatement · cited by 324
- MulEquiv.toMonoidHomproof · cited by 126
- MulEquiv.injectiveproof · cited by 36
- orderOf_injectiveproof · cited by 12
Cited by1
Results whose statement or proof uses this declaration.
- MulChar.exists_mulChar_orderOfproof · cited by 1