Mathlib Map

Theorems · Theorem · number theory

Nat.ModEq.dvd

∀ {n a b : ℕ}, a ≡ b [MOD n] → ↑n ∣ ↑b - ↑a

Alias of the forward direction of Nat.modEq_iff_dvd.

Defined in
Mathlib.Data.Nat.ModEq
Cited by
6 results in Mathlib
Foundations
Depth 43 from the axioms · uses propext
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Nat.ModEq.add · cited by 7ModEq.addNat.ModEq.of_dvd · cited by 5ModEq.of_dvdNat.ModEq.sub' · cited by 3ModEq.sub'Pell.matiyasevic · cited by 1Pell.matiyasevicNat.ModEq.eq_of_abs_lt · cited by 1ModEq.eq_of_abs_ltNat.probablePrime_iff_modEq · cited by 0Nat.probablePrime_iff_mod…Nat.ModEq · cited by 225Nat.ModEqNat.modEq_iff_dvd · cited by 10Nat.modEq_iff_dvdModEq.dvdCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by6

Results whose statement or proof uses this declaration.