Theorems · Theorem · number theory
Nat.card_multiples
∀ (n p : ℕ), {e ∈ Finset.range n | p ∣ e + 1}.card = n / pExactly n / p naturals in [1, n] are multiples of p.
See Nat.card_multiples' for an alternative spelling of the statement.
- Defined in
- Mathlib.Data.Nat.Factorization.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- add_zeroproof · cited by 2,707
- Finset.cardstatement and proof · cited by 2,327
- Finset.rangestatement and proof · cited by 1,341
- Finset.filterstatement and proof · cited by 949
- Finset.filter.congr_simpproof · cited by 47
- Finset.card_insert_of_notMemproof · cited by 45
- Finset.range_add_oneproof · cited by 23
- Finset.filter_emptyproof · cited by 23
- Finset.filter_insertproof · cited by 14
- add_iteproof · cited by 4
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.