Theorems · Theorem · group theory
addOrderOf_eq_card_multiples
∀ {G : Type u_1} [inst : AddLeftCancelMonoid G] [inst_1 : Fintype G] {x : G},
addOrderOf x = Fintype.card ↥(AddSubmonoid.multiples x)- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddLeftCancelMonoidFintype
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypestatement and proof · cited by 7,736
- Fintype.cardstatement · cited by 1,386
- AddSubmonoidstatement · cited by 1,178
- Fintype.card_finproof · cited by 270
- addOrderOfstatement and proof · cited by 208
- AddSubmonoid.multiplesstatement · cited by 40
- AddLeftCancelMonoidstatement and proof · cited by 37
- Fintype.card_eqproof · cited by 19
- isOfFinAddOrder_of_finiteproof · cited by 10
- finEquivMultiplesproof · cited by 7
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