Theorems · Theorem · group theory
Multiset.prod_singleton
∀ {M : Type u_3} [inst : CommMonoid M] (a : M), {a}.prod = a- Cited by
- 29 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoid
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_oneproof · cited by 3,885
- Multisetstatement · cited by 2,627
- CommMonoidstatement and proof · cited by 2,264
- Multiset.prodstatement · cited by 528
- Multiset.prod_consproof · cited by 68
Cited by29
Results whose statement or proof uses this declaration.
- Equiv.Perm.sign_of_cycleType'proof · cited by 2
- Multiset.le_prod_of_submultiplicative_on_pred_of_nonnegproof · cited by 2
- PrimeSpectrum.exists_primeSpectrum_prod_le_and_ne_bot_of_domainproof · cited by 1
- Equiv.Perm.card_of_cycleType_singletonproof · cited by 1
- Multiset.esymm_pair_oneproof · cited by 1
- Multiset.esymm_pair_twoproof · cited by 1
- Associates.factors_selfproof · cited by 1
- Complex.coeff_regularizedGaussHGFunSeriesproof · cited by 1
- PrimeMultiset.prod_ofPrimeproof · cited by 1
- Polynomial.Splits.eq_X_sub_C_of_single_rootproof · cited by 1
- Cubic.eq_prod_three_rootsproof · cited by 1
- UniqueFactorizationMonoid.normalizedFactors_prod_eqproof · cited by 0