Rearrangement Operation as Replacement Operations

Example of use of Replacement Operation
Let $\left({a, b, c, d}\right)$ be an ordered quadruple consisting of four variables whose values are to be rearranged into the order $\left({b, c, d, a}\right)$.

This can be implemented using replacement operations.

Let $t$ be a new variable which has been established for this purpose.

Then the sequence of replacement operations:
 * $t \gets a$
 * $a \gets b$
 * $b \gets c$
 * $c \gets d$
 * $d \gets t$

performs the task.

Proof
Observing the values of the variables after each replacement operation:

Hence the result.

Notice how the sequence:
 * $a \gets b, b \gets c, c \gets d, d \gets a$

does not do the job.

This is because, when $d \gets a$ is performed, $a$ no longer contains its original value, and the resulting ordered quadruple is $\left({b, c, d, b}\right)$.