Rule relationalgebra.absorp

Parameters
Buggy	no
Rewrite rule	yes
Siblings

Rewrite rule

r ∩ (r ∪ s)   ⇒   r
r ∩ (s ∪ r)   ⇒   r
(r ∪ s) ∩ r   ⇒   r
(s ∪ r) ∩ r   ⇒   r
r ∪ (r ∩ s)   ⇒   r
r ∪ (s ∩ r)   ⇒   r
(r ∩ s) ∪ r   ⇒   r
(s ∩ r) ∪ r   ⇒   r

Formal Mathematical Properties

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="conj"/><OMV name="$0"/><OMA><OMS cd="relalg" name="disj"/><OMV name="$0"/><OMV name="$1"/></OMA></OMA><OMV name="$0"/></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="conj"/><OMV name="$0"/><OMA><OMS cd="relalg" name="disj"/><OMV name="$1"/><OMV name="$0"/></OMA></OMA><OMV name="$0"/></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="conj"/><OMA><OMS cd="relalg" name="disj"/><OMV name="$0"/><OMV name="$1"/></OMA><OMV name="$0"/></OMA><OMV name="$0"/></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$1"/><OMV name="$0"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="conj"/><OMA><OMS cd="relalg" name="disj"/><OMV name="$1"/><OMV name="$0"/></OMA><OMV name="$0"/></OMA><OMV name="$0"/></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="disj"/><OMV name="$0"/><OMA><OMS cd="relalg" name="conj"/><OMV name="$0"/><OMV name="$1"/></OMA></OMA><OMV name="$0"/></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="disj"/><OMV name="$0"/><OMA><OMS cd="relalg" name="conj"/><OMV name="$1"/><OMV name="$0"/></OMA></OMA><OMV name="$0"/></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="disj"/><OMA><OMS cd="relalg" name="conj"/><OMV name="$0"/><OMV name="$1"/></OMA><OMV name="$0"/></OMA><OMV name="$0"/></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMBIND><OMS cd="quant1" name="forall"/><OMBVAR><OMV name="$1"/><OMV name="$0"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="disj"/><OMA><OMS cd="relalg" name="conj"/><OMV name="$1"/><OMV name="$0"/></OMA><OMV name="$0"/></OMA><OMV name="$0"/></OMA></OMBIND></OMOBJ></FMP>