Rule relationalgebra.remredunexprs

Parameters
Buggy	no
Rewrite rule	yes
Siblings

Rewrite rule

r ∪ V   ⇒   V
V ∪ r   ⇒   V
r ∩ V   ⇒   r
V ∩ r   ⇒   r
V ; V   ⇒   V
r † V   ⇒   V
V † r   ⇒   V
V~   ⇒   V
(V‾)~   ⇒   V‾
r ∪ (V‾)   ⇒   r
(V‾) ∪ r   ⇒   r
r ∩ (V‾)   ⇒   V‾
(V‾) ∩ r   ⇒   V‾
r ; (V‾)   ⇒   V‾
(V‾) ; r   ⇒   V‾
(V‾) † (V‾)   ⇒   V‾
I~   ⇒   I
I ; r   ⇒   r
r ; I   ⇒   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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="disj"/><OMV name="$0"/><OMS cd="relalg" name="universe"/></OMA><OMS cd="relalg" name="universe"/></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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="disj"/><OMS cd="relalg" name="universe"/><OMV name="$0"/></OMA><OMS cd="relalg" name="universe"/></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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="conj"/><OMV name="$0"/><OMS cd="relalg" name="universe"/></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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="conj"/><OMS cd="relalg" name="universe"/><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"><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="comp"/><OMS cd="relalg" name="universe"/><OMS cd="relalg" name="universe"/></OMA><OMS cd="relalg" name="universe"/></OMA></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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="add"/><OMV name="$0"/><OMS cd="relalg" name="universe"/></OMA><OMS cd="relalg" name="universe"/></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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="add"/><OMS cd="relalg" name="universe"/><OMV name="$0"/></OMA><OMS cd="relalg" name="universe"/></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="inv"/><OMS cd="relalg" name="universe"/></OMA><OMS cd="relalg" name="universe"/></OMA></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="inv"/><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA></OMA><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA></OMA></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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="disj"/><OMV name="$0"/><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="disj"/><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="conj"/><OMV name="$0"/><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA></OMA><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA></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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="conj"/><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA><OMV name="$0"/></OMA><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA></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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="comp"/><OMV name="$0"/><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA></OMA><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA></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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="comp"/><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA><OMV name="$0"/></OMA><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA></OMA></OMBIND></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="add"/><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA></OMA><OMA><OMS cd="relalg" name="not"/><OMS cd="relalg" name="universe"/></OMA></OMA></OMOBJ></FMP>

<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd"><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="inv"/><OMS cd="relalg" name="ident"/></OMA><OMS cd="relalg" name="ident"/></OMA></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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="comp"/><OMS cd="relalg" name="ident"/><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"/></OMBVAR><OMA><OMS cd="relation1" name="eq"/><OMA><OMS cd="relalg" name="comp"/><OMV name="$0"/><OMS cd="relalg" name="ident"/></OMA><OMV name="$0"/></OMA></OMBIND></OMOBJ></FMP>