Principle_of_Mathematical_Induction_Well_Ordered_Set

Let $\struct {S, \preceq}$ be a well-ordered set. Let $T \subseteq S$ be a subset of $S$ such that $\forall s \in S: \paren {\forall t \in S: t \prec s \implies t \in T} \implies s \in T$ Then $T = S$.