Theorems · Theorem · number theory
Nat.range_mul_add
∀ (m k : ℕ), (Set.range fun n => m * n + k) = {n | ↑n = ↑k ∧ k ≤ n}The range of (m * · + k) on natural numbers is the set of elements ≥ k in the
residue class of k mod m.
- Defined in
- Mathlib.Data.ZMod.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.ofPredstatement · cited by 6,101
- Set.rangestatement · cited by 4,705
- add_zeroproof · cited by 2,707
- Set.extproof · cited by 2,266
- MulZeroClass.zero_mulproof · cited by 1,625
- add_commproof · cited by 1,535
- ZModstatement and proof · cited by 1,024
- Nat.cast_addproof · cited by 586
- CharP.cast_eq_zeroproof · cited by 357
- Nat.cast_mulproof · cited by 309
- le_iff_exists_addproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- summable_indicator_mod_iff_summableproof · cited by 2