Theorems · Theorem · group theory
Nat.card_units
∀ (α : Type u_1) [inst : GroupWithZero α], Nat.card αˣ = Nat.card α - 1
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finiteproof · cited by 3,029
- Unitsstatement · cited by 2,804
- Nat.cardstatement and proof · cited by 844
- GroupWithZerostatement and proof · cited by 691
- Infiniteproof · cited by 352
- Nat.card_congrproof · cited by 133
- zero_tsubproof · cited by 100
- finite_or_infiniteproof · cited by 50
- Nat.card_eq_zero_of_infiniteproof · cited by 46
- add_tsub_cancel_leftproof · cited by 42
- Equiv.sumComplproof · cited by 23
- Nat.card_uniqueproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- Fintype.card_unitsproof · cited by 9
- FiniteField.unit_isSquare_iffproof · cited by 2
- FiniteField.unitsMap_norm_surjectiveproof · cited by 1
- FiniteField.forall_pow_eq_one_iffproof · cited by 1
- Nat.card_eq_card_units_add_oneproof · cited by 0
- NumberField.torsionOrder_dvd_absNorm_sub_oneproof · cited by 0