Natural Number Multiplication is Associative/Proof 1

Proof
From Index Laws for Semigroup: Product of Indices we have:


 * $+^{z \times y} x = \map {+^z} {+^y x}$

By definition of multiplication, this amounts to:


 * $x \times \paren {z \times y} = \paren {x \times y} \times z$

From Natural Number Multiplication is Commutative, we have:


 * $x \times \paren {z \times y} = x \times \paren {y \times z}$