Theorems · Theorem · group theory
comp_mul_right
∀ {α : Type u_1} [inst : Semigroup α] (x y : α), ((fun x_1 => x_1 * x) ∘ fun x => x * y) = fun x_1 => x_1 * (y * x)Composing two multiplications on the right by y and x
is equal to a multiplication on the right by y * x.
- 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.
- IsRightRegular.mulproof · cited by 3
- Filter.tendsto_cocompact_mul_rightproof · cited by 1
- IsTopologicalGroup.of_nhds_one'proof · cited by 1
- MeasureTheory.Measure.modularCharacterFun_map_mulproof · cited by 0