Theorems · Theorem · group theory
mul_dvd_mul_iff_right
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [IsCancelMulZero α] {a b c : α}, c ≠ 0 → (a * c ∣ b * c ↔ a ∣ b)Given two elements a, b of a commutative cancellative MonoidWithZero and a nonzero
element c, a*c divides b*c iff a divides b.
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 9 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.
- CommMonoidWithZerostatement and proof · cited by 913
- IsCancelMulZerostatement and proof · cited by 177
- mul_right_commproof · cited by 108
- mul_left_inj'proof · cited by 35
Cited by8
Results whose statement or proof uses this declaration.
- Prime.irreducibleproof · cited by 54
- lcm_dvd_iffproof · cited by 6
- IsRadical.squarefreeproof · cited by 6
- Rat.add_den_dvd_lcmproof · cited by 3
- AddCommute.addOrderOf_add_eq_right_of_forall_prime_mul_dvdproof · cited by 2
- Commute.orderOf_mul_eq_right_of_forall_prime_mul_dvdproof · cited by 2
- IsRadical.of_dvdproof · cited by 0
- Algebra.IsUnramifiedAt.not_minpoly_sq_dvdproof · cited by 0