Rule logic.propositional.buggy.defimpl.inv

Parameters
Buggy	yes
Rewrite rule	yes
Siblings

Rewrite rule

(¬p) ∧ q   ⇏   p → q
p ∨ (¬q)   ⇏   p → q
p ∧ (¬q)   ⇏   q → p
(¬p) ∨ q   ⇏   q → p
¬(p ∨ q)   ⇏   p → q

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="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="and"/><OMA><OMS cd="logic1" name="not"/><OMV name="$0"/></OMA><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="implies"/><OMV name="$0"/><OMV name="$1"/></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="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="or"/><OMV name="$0"/><OMA><OMS cd="logic1" name="not"/><OMV name="$1"/></OMA></OMA><OMA><OMS cd="logic1" name="implies"/><OMV name="$0"/><OMV name="$1"/></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="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="and"/><OMV name="$0"/><OMA><OMS cd="logic1" name="not"/><OMV name="$1"/></OMA></OMA><OMA><OMS cd="logic1" name="implies"/><OMV name="$1"/><OMV name="$0"/></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="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="or"/><OMA><OMS cd="logic1" name="not"/><OMV name="$0"/></OMA><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="implies"/><OMV name="$1"/><OMV name="$0"/></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="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="not"/><OMA><OMS cd="logic1" name="or"/><OMV name="$0"/><OMV name="$1"/></OMA></OMA><OMA><OMS cd="logic1" name="implies"/><OMV name="$0"/><OMV name="$1"/></OMA></OMA></OMBIND></OMOBJ></FMP>