Theorems · Theorem · group theory
orderOf_eq_card_of_forall_mem_powers
∀ {α : Type u_1} [inst : Group α] {g : α}, (∀ (x : α), x ∈ Submonoid.powers g) → orderOf g = Nat.card α- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- Submonoidstatement · cited by 3,086
- Nat.cardstatement and proof · cited by 844
- Submonoid.powersstatement and proof · cited by 408
- orderOfstatement · cited by 324
- orderOf_eq_card_of_forall_mem_zpowersproof · cited by 13
- Submonoid.powers_le_zpowersproof · cited by 1
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