Theorems · Theorem · group theory
Commute.mul_mul_mul_comm
∀ {S : Type u_3} [inst : Semigroup S] {b c : S}, Commute b c → ∀ (a d : S), a * b * (c * d) = a * c * (b * d)- Defined in
- Mathlib.Algebra.Group.Commute.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses propext
- Assumes
- Semigroup
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
- Commutestatement and proof · cited by 639
- Semigroupstatement and proof · cited by 202
- Commute.left_commproof · cited by 9
Cited by8
Results whose statement or proof uses this declaration.
- Commute.div_mul_div_commproof · cited by 5
- Commute.add_pow_prime_pow_eqproof · cited by 3
- IsIdempotentElem.mul_of_commuteproof · cited by 3
- isIdempotentElem_one_sub_one_sub_pow_powproof · cited by 1
- Commute.cfcAbs_mul_eqproof · cited by 1
- Finset.noncommProd_mul_distribproof · cited by 0
- IncidenceAlgebra.mu_prod_muproof · cited by 0
- Commute.div_div_div_commproof · cited by 0