Theorems · Theorem · group theory
AddMonoid.minOrder_le_natCard
∀ {G : Type u_1} [inst : AddGroup G] {s : AddSubgroup G}, s ≠ ⊥ → (↑s).Finite → AddMonoid.minOrder G ≤ ↑(Nat.card ↥s)- Defined in
- Mathlib.GroupTheory.Order.Min
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- ENatstatement · cited by 4,985
- Bot.botstatement and proof · cited by 4,720
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Set.Finitestatement and proof · cited by 1,814
- le_rflproof · cited by 1,558
- Nat.cardstatement · cited by 844
- AddMonoid.minOrderstatement · cited by 9
- AddMonoid.le_minOrder_iff_forall_addSubgroupproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- cauchy_davenport_minOrder_addproof · cited by 2
- ZMod.minOrderproof · cited by 1