$xRx'$ and $yRy'$ implies $f(x,y)Rf(x',y')$

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Let $R$ be a binary relation. Is there a name for the following property?

  • $f(x,y)Rf(x',y')\quad$ if $xRx'$ and $yRy'$

Note:$f$ is a function.

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Suggestion: The composition law $f$ is compatible with the binary relation $R$.