Tight closure/Curve/Degree bound for inclusion/Strongly semistable/Fact

Suppose that ${}\operatorname {Syz} {\left(f_{1},\ldots ,f_{n}\right)}$ is strongly semistable.

Then

$R_{m}\subseteq I^{*}{\text{ for }}m\geq {\frac {\sum d_{i}}{n-1}}{\text{ and (for almost all prime numbers) }}R_{m}\cap I^{*}\subseteq I{\text{ for }}m<{\frac {\sum d_{i}}{n-1}}.$

Write a proof