Theorems · Theorem · group theory
comp_mul_left
∀ {α : Type u_1} [inst : Semigroup α] (x y : α), ((fun x_1 => x * x_1) ∘ fun x => y * x) = fun x_1 => x * y * x_1Composing two multiplications on the left by y then x
is equal to a multiplication on the left by x * y.
- Defined in
- Mathlib.Algebra.Group.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext, Quot.sound
- Assumes
- Semigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by4
Results whose statement or proof uses this declaration.
- Commute.orderOf_mul_eq_mul_orderOf_of_coprimeproof · cited by 5
- IsLeftRegular.mulproof · cited by 5
- IsLeftRegular.of_mulproof · cited by 5
- Commute.orderOf_mul_dvd_lcmproof · cited by 4