Definition:Agreement/Relations

Definition
Let:


 * $(1): \quad \RR_1 \subseteq S_1 \times T_1$ be a relation on $S_1 \times T_1$


 * $(2): \quad \RR_2 \subseteq S_2 \times T_2$ be a relation on $S_2 \times T_2$


 * $(3): \quad X \subseteq S_1 \cap S_2$

Let:
 * $\forall s \in X: \map {\RR_1} s = \map {\RR_2} s$

where $\map {\RR_1} s$ denotes the image of $s$ under $\RR$:
 * $\map {\RR_1} s := \set {t \in T: s \mathrel {\RR_1} t}$

Then the relations $\RR_1$ and $\RR_2$ are said to agree on or be in agreement on $X$.