Theorems · Theorem · commutative algebra
orderOf_lt_card
∀ {M₀ : Type u_1} [inst : MonoidWithZero M₀] [Nontrivial M₀] [Finite M₀] (a : M₀), orderOf a < Nat.card M₀- Defined in
- Mathlib.RingTheory.Fintype
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finitestatement and proof · cited by 3,029
- Nontrivialstatement and proof · cited by 2,416
- IsUnitproof · cited by 1,602
- LT.lt.ne'proof · cited by 1,417
- Nat.cardstatement and proof · cited by 844
- LE.le.trans_ltproof · cited by 795
- MonoidWithZerostatement and proof · cited by 456
- orderOfstatement and proof · cited by 324
- Nat.card_posproof · cited by 36
- IsUnit.unit_specproof · cited by 25
- orderOf_unitsproof · cited by 9
- IsUnit.of_pow_eq_oneproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- ZMod.orderOf_ltproof · cited by 0