Rule logic.propositional.buggy.implelim
Parameters | |
Buggy | yes |
Rewrite rule | yes |
Siblings |
Rewrite rule
p → q ⇏ ¬(p ∨ q)p → q ⇏ p ∨ q
p → q ⇏ ¬(p ∧ q)
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="implies"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="not"/><OMA><OMS cd="logic1" name="or"/><OMV name="$0"/><OMV name="$1"/></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="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="implies"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="or"/><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="implies"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="not"/><OMA><OMS cd="logic1" name="and"/><OMV name="$0"/><OMV name="$1"/></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="exists"/><OMBVAR><OMV name="$0"/><OMV name="$1"/></OMBVAR><OMA><OMS cd="relation1" name="neq"/><OMA><OMS cd="logic1" name="implies"/><OMV name="$0"/><OMV name="$1"/></OMA><OMA><OMS cd="logic1" name="or"/><OMV name="$0"/><OMA><OMS cd="logic1" name="not"/><OMV name="$1"/></OMA></OMA></OMA></OMBIND></OMOBJ></FMP>