Theorems · Theorem · group theory
AddSubmonoid.addOrderOf_le_card
∀ {G : Type u_6} [inst : AddGroup G] (s : AddSubmonoid G), (↑s).Finite → ∀ {x : G}, x ∈ s → addOrderOf x ≤ Nat.card ↥s- Defined in
- Mathlib.GroupTheory.OrderOfElement
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement and proof · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- Set.Finitestatement and proof · cited by 1,814
- AddSubmonoidstatement and proof · cited by 1,178
- Nat.cardstatement and proof · cited by 844
- addOrderOfstatement · cited by 208
- Nat.card_monoproof · cited by 5
- AddSubmonoid.multiples_leproof · cited by 4
- Nat.card_addSubmonoidMultiplesproof · cited by 1
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