Theorems · Theorem · group theory
dvd_of_mul_left_eq
∀ {α : Type u_1} [inst : CommSemigroup α] {a b : α} (c : α), c * a = b → a ∣ bAlias of Dvd.intro_left.
- Defined in
- Mathlib.Algebra.Divisibility.Basic
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- CommSemigroup
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.
- CommSemigroupstatement · cited by 62
- Dvd.intro_leftproof · cited by 20
Cited by14
Results whose statement or proof uses this declaration.
- Subgroup.index_dvd_of_leproof · cited by 8
- AddSubgroup.index_dvd_of_leproof · cited by 3
- Subgroup.relIndex_dvd_of_le_leftproof · cited by 3
- AddSubgroup.relIndex_dvd_of_le_leftproof · cited by 2
- Polynomial.Monic.irreducible_iff_irreducible_map_fraction_mapproof · cited by 2
- IsDedekindDomain.map_differentIdeal_dvd_differentIdealproof · cited by 1
- CharP.char_is_prime_of_two_leproof · cited by 1
- Polynomial.Monic.dvd_of_fraction_map_dvd_fraction_mapproof · cited by 1
- IntermediateField.relfinrank_dvd_finrank_botproof · cited by 0
- IntermediateField.relfinrank_dvd_of_le_leftproof · cited by 0
- Subfield.relrank_dvd_of_le_leftproof · cited by 0
- IntermediateField.relrank_dvd_of_le_leftproof · cited by 0