Indicator function in math programming

Question

I have the following doubt:

Being $x$ an integer variable that takes the values $1$, $2$ or $3$. Being $y_1$ a binary variable. Being $y_2$ a binary variable.

I want to express the two following logical constraints:

if $x=2$ then $y_1=1$ if $x=3$ then $y_2=1$

That's all. I have looked around here but usually the constraints are inequalities or continuous variables.

Thanks in advance.

Edit:

I have come up with the following solutions:

$-1y_1=(x-1)(x-3)$
when $x=1 \rightarrow y_1=0$,
when $x=3 \rightarrow y_1=0$,
when $x=2 \rightarrow y_1=1$.

$2y_2=(x-1)(x-2)$
when $x=1 \rightarrow y_2=0$,
when $x=2 \rightarrow y_2=0$,
when $x=3 \rightarrow y_2=1$.

It breaks the linearity, but the constraints are in a Mixed Integer Nonlinear Programming problem.

Could be that a valid solution?

Answer 1

Introduce binary variable $y_0$ and linear constraints: \begin{align} y_0 + y_1 + y_2 &= 1\\ 1y_0 + 2y_1 + 3y_2 &= x \end{align}

Equivalently, eliminating $y_0$: \begin{align} y_1 + y_2 &\le 1\\ 1 + y_1 + 2y_2 &= x \end{align}