Let $U \subseteq \mathbb{R}^n$ be open, let $m \in \mathbb{R}$, and let $P \in \Psi^m(U)$ be elliptic. Suppose $Q_1, Q_2 \in \Psi^{-m}(U)$ are parametrices for $P$, in the two-sided modulo-smoothing sense: for each $j \in \{1,2\}$,
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\begin{align*}
P Q_j - I \in \Psi^{-\infty}(U)
\end{align*}
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and
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\begin{align*}
Q_j P - I \in \Psi^{-\infty}(U),
\end{align*}
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where $I$ denotes the identity operator and the compositions are understood in the pseudodifferential calculus on $U$. Then