 With these additional requirements, the inference patterns for activities and accomplishments follow. Let us first show that Mary was pushing a cart implies Mary pushed a cart. Assume that the first sentence is true in \(w\) with respect to speech time \(S\). Then Mary be pushing a cart is true in \(w\) with respect to an interval \(I\) before \(S\).  According to Definition 3, Mary push a cart is then true in every inertia world \(w' \in IE(w)\) with respect to an interval \(I' \supseteq I\). Because of postulate (20), Mary push a cart is true in every \(w' \in IE(w)\) with respect to interval \(I \ (I\) is a subinterval of \(I')\). Now, the definition of inertia worlds implies that  Mary push a cart is true in \(w\) with respect to interval \(I\). This means that Mary pushed a cart is true in \(w\) with respect to speech time \(S\). 