Theorems · Theorem · number theory
Nat.ModEq.of_mul_left
∀ {n a b : ℕ} (m : ℕ), a ≡ b [MOD m * n] → a ≡ b [MOD n]Cancel left multiplication in the modulus.
For cancelling left multiplication on both sides of the ≡, see nat.modeq.mul_left_cancel'.
- Defined in
- Mathlib.Data.Nat.ModEq
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.ModEqstatement and proof · cited by 225
- Dvd.dvd.transproof · cited by 148
- dvd_mul_leftproof · cited by 47
- Nat.modEq_iff_dvdproof · cited by 10
Cited by4
Results whose statement or proof uses this declaration.
- Nat.odd_of_mod_four_eq_threeproof · cited by 5
- Nat.odd_of_mod_four_eq_oneproof · cited by 4
- Nat.ModEq.of_mul_rightproof · cited by 2
- Nat.modEq_and_modEq_iff_modEq_mulproof · cited by 2