Theorems · Theorem · logic and foundations
Nat.card_zmod
∀ (n : ℕ), Nat.card (ZMod n) = n
- Defined in
- Mathlib.SetTheory.Cardinal.Finite
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ZModstatement · cited by 1,024
- Nat.cardstatement · cited by 844
- Nat.card_eq_fintype_cardproof · cited by 200
- Nat.card_eq_zero_of_infiniteproof · cited by 46
- ZMod.cardproof · cited by 36
Cited by13
Results whose statement or proof uses this declaration.
- Nat.card_zpowersproof · cited by 13
- Nat.card_zmultiplesproof · cited by 11
- IsPrimitiveRoot.zpowers_eqproof · cited by 3
- Submodule.natAbs_det_equivproof · cited by 2
- Subfield.card_botproof · cited by 2
- FiniteField.pow_finrank_eq_natCardproof · cited by 2
- Int.index_zmultiplesproof · cited by 1
- DihedralGroup.card_commute_oddproof · cited by 1
- AddSubgroup.index_range_nsmulproof · cited by 1
- ZMod.minOrderproof · cited by 1
- ZMod.orderOf_ltproof · cited by 0
- finrank_of_isSplittingField_X_pow_sub_Cproof · cited by 0