Left Operation is Associative

Theorem
The left operation is associative:


 * $$\forall x, y, z: \left({x \leftarrow y}\right) \leftarrow z = x \leftarrow \left({y \leftarrow z}\right)$$

Proof
By the definition of the left operation:

$$ $$

$$ $$

Hence the result.

Also see

 * Right Operation is Associative