Theorems · Theorem · group theory
dvd_of_mul_left_dvd
∀ {α : Type u_1} [inst : CommSemigroup α] {a b c : α}, a * b ∣ c → b ∣ c- Defined in
- Mathlib.Algebra.Divisibility.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses propext
- Assumes
- CommSemigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- mul_left_commproof · cited by 184
- CommSemigroupstatement and proof · cited by 62
- Dvd.introproof · cited by 26
- Dvd.elimproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- ModP.preVal_mkproof · cited by 5
- DvdNotUnit.not_isUnitproof · cited by 3
- Pell.matiyasevicproof · cited by 1
- ClassGroup.exists_mk0_eq_mk0proof · cited by 1
- Pell.dvd_of_ysq_dvdproof · cited by 1
- IsFractionRing.associated_den_num_invproof · cited by 1
- Nat.primeFactors_div_gcdproof · cited by 1
- ZMod.isSquare_neg_one_iff'proof · cited by 0