Theorems · Theorem · group theory
dvd_antisymm
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [IsCancelMulZero α] {a b : α} [Subsingleton αˣ], a ∣ b → b ∣ a → a = b- Cited by
- 23 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Unitsstatement and proof · cited by 2,804
- mul_assocproof · cited by 1,667
- MulZeroClass.zero_mulproof · cited by 1,625
- CommMonoidWithZerostatement and proof · cited by 913
- IsCancelMulZerostatement and proof · cited by 177
- mul_eq_oneproof · cited by 6
- mul_right_eq_self₀proof · cited by 1
Cited by23
Results whose statement or proof uses this declaration.
- Dvd.dvd.antisymmproof · cited by 6
- HasEnoughRootsOfUnity.natCard_rootsOfUnityproof · cited by 5
- IsDedekindDomain.differentIdeal_eq_map_differentIdealproof · cited by 3
- ArithmeticFunction.carmichael_lcmproof · cited by 2
- Monoid.exponent_prodproof · cited by 2
- Nat.Coprime.mul_injOn_divisorsproof · cited by 1
- Nat.Prime.pow_injproof · cited by 1
- AddMonoid.exponent_prodproof · cited by 1
- Monoid.exponent_eq_prime_iffproof · cited by 1
- Nat.gcd_greatestproof · cited by 1
- ArithmeticFunction.carmichael_two_pow_of_ne_twoproof · cited by 1
- Group.isCyclic_of_coprime_card_range_card_kerproof · cited by 1