Theorems · Theorem · group theory
mul_dvd_mul_iff_left
∀ {α : Type u_1} [inst : MonoidWithZero α] [IsLeftCancelMulZero α] {a b c : α}, a ≠ 0 → (a * b ∣ a * c ↔ b ∣ c)Given two elements b, c of a cancellative MonoidWithZero and a nonzero element a,
a*b divides a*c iff b divides c.
- Cited by
- 24 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.
- mul_assocproof · cited by 1,667
- MonoidWithZerostatement and proof · cited by 456
- mul_right_inj'proof · cited by 56
- IsLeftCancelMulZerostatement and proof · cited by 48
Cited by24
Results whose statement or proof uses this declaration.
- Prime.irreducibleproof · cited by 54
- lcm_dvd_iffproof · cited by 6
- dvd_prime_powproof · cited by 6
- gcd_mul_left'proof · cited by 4
- gcd_mul_leftproof · cited by 2
- lcm_mul_leftproof · cited by 2
- Ideal.count_associates_eqproof · cited by 2
- modularCyclotomicCharacter.pow_dvd_aux_pow_sub_aux_powproof · cited by 2
- Prime.pow_dvd_of_dvd_mul_leftproof · cited by 2
- Ideal.finprod_not_dvdproof · cited by 1
- divRadical_dvd_derivativeproof · cited by 1
- pow_dvd_pow_iffproof · cited by 1