Theorems · Theorem · group theory
addOrderOf_eq_card_of_forall_mem_multiples
∀ {α : Type u_1} [inst : AddGroup α] {g : α}, (∀ (x : α), x ∈ AddSubmonoid.multiples g) → addOrderOf g = Nat.card α- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubmonoidstatement · cited by 1,178
- Nat.cardstatement and proof · cited by 844
- addOrderOfstatement · cited by 208
- AddSubmonoid.multiplesstatement and proof · cited by 40
- addOrderOf_eq_card_of_forall_mem_zmultiplesproof · cited by 8
- AddSubmonoid.multiples_le_zmultiplesproof · cited by 1
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