Theorems · Theorem · group theory
dvd_mul_left
∀ {α : Type u_1} [inst : CommSemigroup α] (a b : α), a ∣ b * a- Defined in
- Mathlib.Algebra.Divisibility.Basic
- Cited by
- 47 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- CommSemigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- CommSemigroupstatement and proof · cited by 62
- Dvd.introproof · cited by 26
Cited by47
Results whose statement or proof uses this declaration.
- Subgroup.card_subgroup_dvd_cardproof · cited by 8
- Polynomial.coeff_expand_mulproof · cited by 5
- Polynomial.C_mul_dvdproof · cited by 4
- Nat.totient_prime_pow_succproof · cited by 4
- Nat.ModEq.of_mul_leftproof · cited by 4
- IsCoprime.dvd_of_dvd_mul_rightproof · cited by 4
- PNat.gcd_eqproof · cited by 4
- Nat.ModEq.mul_leftproof · cited by 3
- IsCoprime.dvd_of_dvd_mul_leftproof · cited by 3
- AddSubgroup.card_addSubgroup_dvd_cardproof · cited by 3
- IsRelPrime.mul_leftproof · cited by 3
- Polynomial.Monic.irreducible_iff_lt_natDegree_ltproof · cited by 3