Theorems · Theorem · group theory
dvd_mul_of_dvd_left
∀ {α : Type u_1} [inst : Semigroup α] {a b : α}, a ∣ b → ∀ (c : α), a ∣ b * c- Defined in
- Mathlib.Algebra.Divisibility.Basic
- Cited by
- 25 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- Semigroup
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.
- Semigroupstatement and proof · cited by 202
- Dvd.dvd.transproof · cited by 148
- dvd_mul_rightproof · cited by 89
Cited by25
Results whose statement or proof uses this declaration.
- Prime.irreducibleproof · cited by 54
- Dvd.dvd.mul_rightproof · cited by 15
- minpoly.isIntegrallyClosed_dvdproof · cited by 9
- IsRelPrime.of_add_mul_left_leftproof · cited by 5
- Prime.dvd_mulproof · cited by 4
- IsRelPrime.of_mul_left_leftproof · cited by 4
- isRadical_iff_pow_one_ltproof · cited by 3
- divRadical_dvd_wronskian_leftproof · cited by 2
- Nat.Coprime.dvd_mul_rightproof · cited by 2
- Squarefree.of_mul_leftproof · cited by 2
- divRadical_dvd_derivativeproof · cited by 1