Rule logic.propositional.absorpand

Parameters
Buggy	no
Rewrite rule	yes
Siblings	logic.propositional.absorption

Rewrite rule

p ∧ (p ∨ q)   ⇒   p
p ∧ (q ∨ p)   ⇒   p
(p ∨ q) ∧ p   ⇒   p
(q ∨ p) ∧ p   ⇒   p

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="logic1" name="and"/><OMV name="$0"/><OMA><OMS cd="logic1" name="or"/><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="logic1" name="and"/><OMV name="$0"/><OMA><OMS cd="logic1" name="or"/><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="logic1" name="and"/><OMA><OMS cd="logic1" name="or"/><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="logic1" name="and"/><OMA><OMS cd="logic1" name="or"/><OMV name="$1"/><OMV name="$0"/></OMA><OMV name="$0"/></OMA><OMV name="$0"/></OMA></OMBIND></OMOBJ></FMP>