Rule logic.propositional.absorpor
Parameters | |
Buggy | no |
Rewrite rule | yes |
Siblings | logic.propositional.absorption |
Rewrite rule
p ∨ (p ∧ q) ⇒ pp ∨ (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="or"/><OMV name="$0"/><OMA><OMS cd="logic1" name="and"/><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="or"/><OMV name="$0"/><OMA><OMS cd="logic1" name="and"/><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="or"/><OMA><OMS cd="logic1" name="and"/><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="or"/><OMA><OMS cd="logic1" name="and"/><OMV name="$1"/><OMV name="$0"/></OMA><OMV name="$0"/></OMA><OMV name="$0"/></OMA></OMBIND></OMOBJ></FMP>