Theorems · Theorem · group theory
Monoid.le_minOrder_iff_forall_subgroup
∀ {G : Type u_1} [inst : Group G] {n : ℕ∞},
n ≤ Monoid.minOrder G ↔ ∀ ⦃s : Subgroup G⦄, s ≠ ⊥ → (↑s).Finite → n ≤ ↑(Nat.card ↥s)- Defined in
- Mathlib.GroupTheory.Order.Min
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Groupstatement and proof · cited by 6,238
- ENatstatement and proof · cited by 4,985
- Bot.botstatement and proof · cited by 4,720
- Subgroupstatement and proof · cited by 3,593
- LE.le.transproof · cited by 3,151
- Set.Finitestatement and proof · cited by 1,814
- Nat.cardstatement and proof · cited by 844
- orderOfproof · cited by 324
- Set.Finite.subsetproof · cited by 285
- Subgroup.zpowersproof · cited by 204
- IsOfFinOrderproof · cited by 113
Cited by1
Results whose statement or proof uses this declaration.
- Monoid.minOrder_le_natCardproof · cited by 1