# Help with formulating an implication

I have a binary variable $$y$$ and a set of binary variables $$x_i$$, where $$i\in I$$. My problem requires that $$\sum\limits_{i\in I}x_i = b.$$ What I want to formulate is the following implication: if $$\sum\limits_{i\in \tilde{I}} x_i \leq b-1$$ then $$y=1$$ where $$\tilde{I}\subseteq I$$, but I can't seem to figure out how. I have been able to find a formulation that says if $$\sum\limits_{i\in \tilde{I}}x_i=m$$ then $$y=0$$ by the inequality $$\sum\limits_{i\in \tilde{I}}x_i + y \leq m$$ but that is not exactly what I want. Any help is greatly appreciated!

$$x_i \le y$$ for $$i\in I \setminus \tilde{I}$$