Rule logic.propositional.andoveror

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

Rewrite rule

p ∧ (q ∨ r)   ⇒   (p ∧ q) ∨ (p ∧ r)
(p ∨ q) ∧ r   ⇒   (p ∧ r) ∨ (q ∧ 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"/><OMV name="$2"/></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="$2"/></OMA></OMA><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="and"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="and"/><OMV name="$0"/><OMV name="$2"/></OMA></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"/><OMV name="$1"/><OMV name="$2"/></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="$2"/></OMA><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="and"/><OMV name="$0"/><OMV name="$2"/></OMA><OMA><OMS cd="logic1" name="and"/><OMV name="$1"/><OMV name="$2"/></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>