Theorems · Theorem · commutative algebra
natCard_units_lt
∀ (M₀ : Type u_1) [inst : MonoidWithZero M₀] [Nontrivial M₀] [Finite M₀], Nat.card M₀ˣ < Nat.card M₀
- Defined in
- Mathlib.RingTheory.Fintype
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fintypeproof · cited by 7,736
- Finitestatement and proof · cited by 3,029
- Unitsstatement · cited by 2,804
- Nontrivialstatement and proof · cited by 2,416
- Nat.cardstatement · cited by 844
- MonoidWithZerostatement and proof · cited by 456
- Fintype.ofFiniteproof · cited by 255
- Fintype.card_eq_nat_cardproof · cited by 31
- card_units_ltproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- orderOf_lt_cardproof · cited by 1