\begin{definition}[Definition:Agreement/Mappings]
Let:
:$(1): \quad f_1: S_1 \to T_1$ be a mapping from $S_1$ to $T_1$
:$(2): \quad f_2: S_2 \to T_2$ be a mapping from $S_2$ to $T_2$
:$(3): \quad X \subseteq S_1 \cap S_2$
Let:
:$\forall s \in X: \map {f_1} s = \map {f_2} s$
Then the mappings $f_1$ and $f_2$ are said to '''agree on''' or '''be in agreement on''' $X$.
\end{definition}