app'app'minusx0xapp'app'minusapp'sxapp'syapp'app'minusxyapp'app'minusapp'app'minusxyzapp'app'minusxapp'app'plusyzapp'app'quot0app'sy0app'app'quotapp'sxapp'syapp'sapp'app'quotapp'app'minusxyapp'syapp'app'plus0yyapp'app'plusapp'sxyapp'sapp'app'plusxyapp'app'appnilkkapp'app'applnillapp'app'appapp'app'consxlkapp'app'consxapp'app'applkapp'sumapp'app'consxnilapp'app'consxnilapp'sumapp'app'consxapp'app'consylapp'sumapp'app'consapp'app'plusxylapp'sumapp'app'applapp'app'consxapp'app'consykapp'sumapp'app'applapp'sumapp'app'consxapp'app'consykapp'app'mapfnilnilapp'app'mapfapp'app'consxxsapp'app'consapp'fxapp'app'mapfxsapp'app'filterfnilnilapp'app'filterfapp'app'consxxsapp'app'app'app'filter2app'fxfxxsapp'app'app'app'filter2truefxxsapp'app'consxapp'app'filterfxsapp'app'app'app'filter2falsefxxsapp'app'filterfxs2.1app'minus0minusminus1minus2000s0ss1plus0plusplus1plus2quot0quotquot1quot2app0appapp1app2nil0nilcons0conscons1cons2sum0sumsum1map0mapmap1map2filter0filterfilter1filter3filter20filter2filter21filter22filter23filter24true0truefalse0falseapp'minusy1minus1y1app'minus1x0y1minus2x0y1app'sy1s1y1app'plusy1plus1y1app'plus1x0y1plus2x0y1app'quoty1quot1y1app'quot1x0y1quot2x0y1app'appy1app1y1app'app1x0y1app2x0y1app'consy1cons1y1app'cons1x0y1cons2x0y1app'sumy1sum1y1app'mapy1map1y1app'map1x0y1map2x0y1app'filtery1filter1y1app'filter1x0y1filter3x0y1app'filter2y1filter21y1app'filter21x0y1filter22x0y1app'filter22x0x1y1filter23x0x1y1app'filter23x0x1x2y1filter24x0x1x2y1minus2x0xminus2s1xs1yminus2xyminus2minus2xyzminus2xplus2yzquot20s1y0quot2s1xs1ys1quot2minus2xys1yplus20yyplus2s1xys1plus2xyapp2nilkkapp2lnillapp2cons2xlkcons2xapp2lksum1cons2xnilcons2xnilsum1cons2xcons2ylsum1cons2plus2xylsum1app2lcons2xcons2yksum1app2lsum1cons2xcons2ykmap2fnilnilmap2fcons2xxscons2app'fxmap2fxsfilter3fnilnilfilter3fcons2xxsfilter24app'fxfxxsfilter24truefxxscons2xfilter3fxsfilter24falsefxxsfilter3fxsapp'minusy1minus1y1app'minus1x0y1minus2x0y1app'sy1s1y1app'plusy1plus1y1app'plus1x0y1plus2x0y1app'quoty1quot1y1app'quot1x0y1quot2x0y1app'appy1app1y1app'app1x0y1app2x0y1app'consy1cons1y1app'cons1x0y1cons2x0y1app'sumy1sum1y1app'mapy1map1y1app'map1x0y1map2x0y1app'filtery1filter1y1app'filter1x0y1filter3x0y1app'filter2y1filter21y1app'filter21x0y1filter22x0y1app'filter22x0x1y1filter23x0x1y1app'filter23x0x1x2y1filter24x0x1x2y1minus2s1xs1yminus2xyminus2minus2xyzminus2xplus2yzminus2minus2xyzplus2yzquot2s1xs1yquot2minus2xys1yquot2s1xs1yminus2xyplus2s1xyplus2xyapp2cons2xlkapp2lksum1cons2xcons2ylsum1cons2plus2xylsum1cons2xcons2ylplus2xysum1app2lcons2xcons2yksum1app2lsum1cons2xcons2yksum1app2lcons2xcons2ykapp2lsum1cons2xcons2yksum1app2lcons2xcons2yksum1cons2xcons2ykmap2fcons2xxsapp'fxmap2fcons2xxsmap2fxsfilter3fcons2xxsfilter24app'fxfxxsfilter3fcons2xxsapp'fxfilter24truefxxsfilter3fxsfilter24falsefxxsfilter3fxsapp'minus1x0y1minus2x0y1app'plus1x0y1plus2x0y1app'quot1x0y1quot2x0y1app'app1x0y1app2x0y1app'sumy1sum1y1app'map1x0y1map2x0y1app'filter1x0y1filter3x0y1app'filter23x0x1x2y1filter24x0x1x2y1trueapp'map1x0y1map2x0y1map2fcons2xxsapp'fxapp'filter1x0y1filter3x0y1filter3fcons2xxsfilter24app'fxfxxsfilter24truefxxsfilter3fxsfilter3fcons2xxsapp'fxapp'filter23x0x1x2y1filter24x0x1x2y1filter24falsefxxsfilter3fxsmap2fcons2xxsmap2fxstruemap2fcons2xxsapp'fx1false12true2map2fcons2xxsmap2fxs1false12true2filter3fcons2xxsapp'fx1false12true2app'map1x0y1map2x0y11true12false2filter3fcons2xxsfilter24app'fxfxxs1false22true32true4app'filter1x0y1filter3x0y11true12false2app'filter23x0x1x2y1filter24x0x1x2y11true11true21true32false4filter24truefxxsfilter3fxs2false14false2filter24falsefxxsfilter3fxs2false14false2app'quot1x0y1quot2x0y1falseapp'sumy1sum1y1falsequot2s1xs1yquot2minus2xys1ytrue1s1111quot221s111minus221minus2x0xminus2minus2xyzminus2xplus2yzminus2s1xs1yminus2xysum1app2lcons2xcons2yksum1app2lsum1cons2xcons2yktrue1sum1111cons221112plus221112app221112nil00000s1111sum1111sum1app2lcons2xcons2yksum1app2lsum1cons2xcons2yksum1cons2xcons2ylsum1cons2plus2xylapp2nilkkapp2lnillapp2cons2xlkcons2xapp2lkplus20yyplus2s1xys1plus2xysum1cons2xnilcons2xnilsum1cons2xcons2ylsum1cons2plus2xylapp2nilkkapp2lnillapp2cons2xlkcons2xapp2lkplus20yyplus2s1xys1plus2xysum1cons2xnilcons2xnil1sum1111cons221112plus221112app222112nil00000s1111sum1111sum1app2lcons2xcons2yksum1app2lsum1cons2xcons2yksum1cons2xcons2ylsum1cons2plus2xylapp2nilkkapp2lnillapp2cons2xlkcons2xapp2lkplus2s1xys1plus2xysum1cons2xnilcons2xnilsum1cons2xcons2ylsum1cons2plus2xylapp2nilkkapp2lnillapp2cons2xlkcons2xapp2lkplus20yyplus2s1xys1plus2xysum1cons2xnilcons2xnil1sum1111cons222112plus221112app222122nil02s1111sum1121sum1app2lcons2xcons2yksum1app2lsum1cons2xcons2yksum1cons2xcons2ylsum1cons2plus2xylapp2cons2xlkcons2xapp2lkplus2s1xys1plus2xysum1cons2xnilcons2xnil1sum1111cons2221112plus221112app222112s1111nil00sum1121sum1app2lcons2xcons2yksum1app2lsum1cons2xcons2ykplus2s1xys1plus2xysum1cons2xnilcons2xnil20sum1cons2x0nil1cons2212sum1101sum111app222cons22sum11quot2s1xs1yminus2xyfalseapp'minus1x0y1minus2x0y1falsesum1app2lcons2xcons2yksum1cons2xcons2ykfalseminus2minus2xyzminus2xplus2yzminus2s1xs1yminus2xytrue1plus221112000s1111minus221112minus221112minus2minus2xyzminus2xplus2yzminus2s1xs1yminus2xyplus20yyplus2s1xys1plus2xyplus20yyplus2s1xys1plus2xy20minus2minus2xyzminus2xplus2yz1true1minus2s1xs1yminus2xy1true12true2sum1cons2xcons2ylsum1cons2plus2xyltrue1plus221112000s1111cons221112sum1111sum1cons2xcons2ylsum1cons2plus2xylplus20yyplus2s1xys1plus2xyplus20yyplus2s1xys1plus2xy201plus221112000s1111sum1121cons2211122plus2s1xys1plus2xyplus20yyplus2s1xys1plus2xyminus2minus2xyzplus2yzfalsesum1cons2xcons2ylplus2xyfalseapp'plus1x0y1plus2x0y1falsesum1app2lcons2xcons2ykapp2lsum1cons2xcons2ykfalseapp'app1x0y1app2x0y1falseplus2s1xyplus2xytrue1s1111plus221112plus2s1xyplus2xyplus2s1xyplus2xy1true12false2app2cons2xlkapp2lktrue1cons221112app221112app2cons2xlkapp2lkapp2cons2xlkapp2lk1true12false2AProVEAProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Statistics for single proof: 100.00 % (26 real / 0 unknown / 0 assumptions / 26 total proof steps)http://aprove.informatik.rwth-aachen.deJohnDoe