Theorems · Theorem · number theory
Nat.ModEq.comm
∀ {n a b : ℕ}, a ≡ b [MOD n] ↔ b ≡ a [MOD n]- Defined in
- Mathlib.Data.Nat.ModEq
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.ModEqstatement · cited by 225
- Nat.ModEq.symmproof · cited by 29
Cited by11
Results whose statement or proof uses this declaration.
- pow_eq_pow_iff_modEqproof · cited by 5
- nsmul_eq_nsmul_iff_modEqproof · cited by 4
- RightCancelMonoid.pow_eq_pow_iff_modEqproof · cited by 3
- AddRightCancelMonoid.nsmul_eq_nsmul_iff_modEqproof · cited by 3
- Nat.left_modEq_add_iffproof · cited by 1
- CharP.natCast_eq_natCastproof · cited by 1
- IsOfFinAddOrder.nsmul_eq_nsmul_iff_modEqproof · cited by 1
- pow_pow_modEq_oneproof · cited by 1
- IsOfFinOrder.pow_eq_pow_iff_modEqproof · cited by 1
- Nat.right_modEq_add_iffproof · cited by 0
- Nat.probablePrime_iff_modEqproof · cited by 0