instCommSemigroup — Mathlib

English

The associativity of multiplication on Ico(0,1) is verified: (xy)z = x(yz) for x,y,z ∈ Ico(0,1).

Русский

Проверена ассоциативность умножения на Ico(0,1): (xy)z = x(yz) для x,y,z ∈ Ico(0,1).

LaTeX

$$$\forall x,y,z \in Ico(0,1),\; (x y) z = x (y z)$$$

Lean4

instance instCommSemigroup {R : Type*} [CommSemiring R] [PartialOrder R] [IsOrderedRing R] :
    CommSemigroup (Ico (0 : R) 1) :=
  fast_instance%Subtype.coe_injective.commSemigroup _ coe_mul

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