app'app'eq00trueapp'app'eq0app'sxfalseapp'app'eqapp'sx0falseapp'app'eqapp'sxapp'syapp'app'eqxyapp'app'le0ytrueapp'app'leapp'sx0falseapp'app'leapp'sxapp'syapp'app'lexyapp'app'appnilyyapp'app'appapp'app'addnxyapp'app'addnapp'app'appxyapp'minapp'app'addnnilnapp'minapp'app'addnapp'app'addmxapp'app'if_minapp'app'lenmapp'app'addnapp'app'addmxapp'app'if_mintrueapp'app'addnapp'app'addmxapp'minapp'app'addnxapp'app'if_minfalseapp'app'addnapp'app'addmxapp'minapp'app'addmxapp'app'rmnnilnilapp'app'rmnapp'app'addmxapp'app'app'if_rmapp'app'eqnmnapp'app'addmxapp'app'app'if_rmtruenapp'app'addmxapp'app'rmnxapp'app'app'if_rmfalsenapp'app'addmxapp'app'addmapp'app'rmnxapp'app'minsortnilnilnilapp'app'minsortapp'app'addnxyapp'app'app'if_minsortapp'app'eqnapp'minapp'app'addnxapp'app'addnxyapp'app'app'if_minsorttrueapp'app'addnxyapp'app'addnapp'app'minsortapp'app'appapp'app'rmnxynilapp'app'app'if_minsortfalseapp'app'addnxyapp'app'minsortxapp'app'addnyapp'app'mapfnilnilapp'app'mapfapp'app'addxxsapp'app'addapp'fxapp'app'mapfxsapp'app'filterfnilnilapp'app'filterfapp'app'addxxsapp'app'app'app'filter2app'fxfxxsapp'app'app'app'filter2truefxxsapp'app'addxapp'app'filterfxsapp'app'app'app'filter2falsefxxsapp'app'filterfxs2.1app'eq0eqeq1eq2000true0trues0ss1false0falsele0lele1le2app0appapp1app2nil0niladd0addadd1add2min0minmin1if_min0if_minif_min1if_min2rm0rmrm1rm2if_rm0if_rmif_rm1if_rm2if_rm3minsort0minsortminsort1minsort2if_minsort0if_minsortif_minsort1if_minsort2if_minsort3map0mapmap1map2filter0filterfilter1filter3filter20filter2filter21filter22filter23filter24app'eqy1eq1y1app'eq1x0y1eq2x0y1app'sy1s1y1app'ley1le1y1app'le1x0y1le2x0y1app'appy1app1y1app'app1x0y1app2x0y1app'addy1add1y1app'add1x0y1add2x0y1app'miny1min1y1app'if_miny1if_min1y1app'if_min1x0y1if_min2x0y1app'rmy1rm1y1app'rm1x0y1rm2x0y1app'if_rmy1if_rm1y1app'if_rm1x0y1if_rm2x0y1app'if_rm2x0x1y1if_rm3x0x1y1app'minsorty1minsort1y1app'minsort1x0y1minsort2x0y1app'if_minsorty1if_minsort1y1app'if_minsort1x0y1if_minsort2x0y1app'if_minsort2x0x1y1if_minsort3x0x1y1app'mapy1map1y1app'map1x0y1map2x0y1app'filtery1filter1y1app'filter1x0y1filter3x0y1app'filter2y1filter21y1app'filter21x0y1filter22x0y1app'filter22x0x1y1filter23x0x1y1app'filter23x0x1x2y1filter24x0x1x2y1eq200trueeq20s1xfalseeq2s1x0falseeq2s1xs1yeq2xyle20ytruele2s1x0falsele2s1xs1yle2xyapp2nilyyapp2add2nxyadd2napp2xymin1add2nnilnmin1add2nadd2mxif_min2le2nmadd2nadd2mxif_min2trueadd2nadd2mxmin1add2nxif_min2falseadd2nadd2mxmin1add2mxrm2nnilnilrm2nadd2mxif_rm3eq2nmnadd2mxif_rm3truenadd2mxrm2nxif_rm3falsenadd2mxadd2mrm2nxminsort2nilnilnilminsort2add2nxyif_minsort3eq2nmin1add2nxadd2nxyif_minsort3trueadd2nxyadd2nminsort2app2rm2nxynilif_minsort3falseadd2nxyminsort2xadd2nymap2fnilnilmap2fadd2xxsadd2app'fxmap2fxsfilter3fnilnilfilter3fadd2xxsfilter24app'fxfxxsfilter24truefxxsadd2xfilter3fxsfilter24falsefxxsfilter3fxsapp'eqy1eq1y1app'eq1x0y1eq2x0y1app'sy1s1y1app'ley1le1y1app'le1x0y1le2x0y1app'appy1app1y1app'app1x0y1app2x0y1app'addy1add1y1app'add1x0y1add2x0y1app'miny1min1y1app'if_miny1if_min1y1app'if_min1x0y1if_min2x0y1app'rmy1rm1y1app'rm1x0y1rm2x0y1app'if_rmy1if_rm1y1app'if_rm1x0y1if_rm2x0y1app'if_rm2x0x1y1if_rm3x0x1y1app'minsorty1minsort1y1app'minsort1x0y1minsort2x0y1app'if_minsorty1if_minsort1y1app'if_minsort1x0y1if_minsort2x0y1app'if_minsort2x0x1y1if_minsort3x0x1y1app'mapy1map1y1app'map1x0y1map2x0y1app'filtery1filter1y1app'filter1x0y1filter3x0y1app'filter2y1filter21y1app'filter21x0y1filter22x0y1app'filter22x0x1y1filter23x0x1y1app'filter23x0x1x2y1filter24x0x1x2y110eq2s1xs1yeq2xyle2s1xs1yle2xyapp2add2nxyapp2xymin1add2nadd2mxif_min2le2nmadd2nadd2mxmin1add2nadd2mxle2nmif_min2trueadd2nadd2mxmin1add2nxif_min2falseadd2nadd2mxmin1add2mxrm2nadd2mxif_rm3eq2nmnadd2mxrm2nadd2mxeq2nmif_rm3truenadd2mxrm2nxif_rm3falsenadd2mxrm2nxminsort2add2nxyif_minsort3eq2nmin1add2nxadd2nxyminsort2add2nxyeq2nmin1add2nxminsort2add2nxymin1add2nxif_minsort3trueadd2nxyminsort2app2rm2nxynilif_minsort3trueadd2nxyapp2rm2nxyif_minsort3trueadd2nxyrm2nxif_minsort3falseadd2nxyminsort2xadd2nymap2fadd2xxsapp'fxmap2fadd2xxsmap2fxsfilter3fadd2xxsfilter24app'fxfxxsfilter3fadd2xxsapp'fxfilter24truefxxsfilter3fxsfilter24falsefxxsfilter3fxsapp'eq1x0y1eq2x0y1app'le1x0y1le2x0y1app'app1x0y1app2x0y1app'miny1min1y1app'if_min1x0y1if_min2x0y1app'rm1x0y1rm2x0y1app'if_rm2x0x1y1if_rm3x0x1y1app'minsort1x0y1minsort2x0y1app'if_minsort2x0x1y1if_minsort3x0x1y1app'map1x0y1map2x0y1app'filter1x0y1filter3x0y1app'filter23x0x1x2y1filter24x0x1x2y1trueapp'map1x0y1map2x0y1map2fadd2xxsapp'fxapp'filter1x0y1filter3x0y1filter3fadd2xxsfilter24app'fxfxxsfilter24truefxxsfilter3fxsfilter3fadd2xxsapp'fxapp'filter23x0x1x2y1filter24x0x1x2y1filter24falsefxxsfilter3fxsmap2fadd2xxsmap2fxstruemap2fadd2xxsapp'fx1false12true2map2fadd2xxsmap2fxs1false12true2filter3fadd2xxsapp'fx1false12true2app'map1x0y1map2x0y11true12false2filter3fadd2xxsfilter24app'fxfxxs1false22true32true4app'filter1x0y1filter3x0y11true12false2app'filter23x0x1x2y1filter24x0x1x2y11true11true21true32false4filter24truefxxsfilter3fxs2false14false2filter24falsefxxsfilter3fxs2false14false2app'if_minsort2x0x1y1if_minsort3x0x1y1falseapp'minsort1x0y1minsort2x0y1falseif_minsort3trueadd2nxyminsort2app2rm2nxynilminsort2add2nxyif_minsort3eq2nmin1add2nxadd2nxyif_minsort3falseadd2nxyminsort2xadd2nytruemin1add2nnilnmin1add2nadd2mxif_min2le2nmadd2nadd2mxif_min2trueadd2nadd2mxmin1add2nxif_min2falseadd2nadd2mxmin1add2mxeq200trueeq20s1xfalseeq2s1x0falseeq2s1xs1yeq2xyle20ytruele2s1x0falsele2s1xs1yle2xyrm2nnilnilrm2nadd2mxif_rm3eq2nmnadd2mxif_rm3truenadd2mxrm2nxapp2nilyyapp2add2nxyadd2napp2xyif_rm3falsenadd2mxadd2mrm2nxeq200eq20s1x0eq2s1x00eq2s1x0s1x1le20x0le2s1x00le2s1x0s1x1app2nilx0app2add2x0x1x2min1add2x0nilmin1add2x0add2x1x2if_min2trueadd2x0add2x1x2if_min2falseadd2x0add2x1x2rm2x0nilrm2x0add2x1x2if_rm3truex0add2x1x2if_rm3falsex0add2x1x21minsort22-22122app2212rm222nil00add2222if_rm33213eq22-2true00if_minsort33-22223min11-2if_min22-22le220false00000s110minsort2add2nxyif_minsort3eq2nmin1add2nxadd2nxyif_minsort3falseadd2nxyminsort2xadd2nyrm2nnilnilrm2nadd2mxif_rm3eq2nmnadd2mxif_rm3truenadd2mxrm2nxapp2nilyyapp2add2nxyadd2napp2xyeq200trueeq20s1xfalseeq2s1x0falseeq2s1xs1yeq2xyif_rm3falsenadd2mxadd2mrm2nxmin1add2nnilnmin1add2nadd2mxif_min2le2nmadd2nadd2mxif_min2trueadd2nadd2mxmin1add2nxif_min2falseadd2nadd2mxmin1add2mxeq200trueeq20s1xfalseeq2s1x0falseeq2s1xs1yeq2xyle20ytruele2s1x0falsele2s1xs1yle2xyeq200eq20s1x0eq2s1x00eq2s1x0s1x1le20x0le2s1x00le2s1x0s1x1min1add2x0nilmin1add2x0add2x1x2if_min2trueadd2x0add2x1x2if_min2falseadd2x0add2x1x2if_minsort3falseadd2nxyminsort2xadd2ny2true1minsort2add2nxyif_minsort3eq2nmin1add2nxadd2nxy1false22false3app'if_rm2x0x1y1if_rm3x0x1y1falseif_minsort3trueadd2nxyrm2nxfalseapp'rm1x0y1rm2x0y1falseapp'if_min1x0y1if_min2x0y1falseminsort2add2nxymin1add2nxfalseapp'miny1min1y1falserm2nadd2mxif_rm3eq2nmnadd2mxif_rm3truenadd2mxrm2nxif_rm3falsenadd2mxrm2nxtrueeq200trueeq20s1xfalseeq2s1x0falseeq2s1xs1yeq2xyeq200eq20s1x0eq2s1x00eq2s1x0s1x1rm2nadd2mxif_rm3eq2nmnadd2mx1false22false3if_rm3truenadd2mxrm2nx2false13true2if_rm3falsenadd2mxrm2nx2false13true2min1add2nadd2mxif_min2le2nmadd2nadd2mxif_min2trueadd2nadd2mxmin1add2nxif_min2falseadd2nadd2mxmin1add2mxtruele20ytruele2s1x0falsele2s1xs1yle2xyle20x0le2s1x00le2s1x0s1x11add2211min111add222if_min222min1add2nadd2mxif_min2le2nmadd2nadd2mxmin1add2nadd2mxif_min2le2nmadd2nadd2mx1false2rm2nadd2mxeq2nmfalseminsort2add2nxyeq2nmin1add2nxfalseapp'eq1x0y1eq2x0y1falsemin1add2nadd2mxle2nmfalseapp'le1x0y1le2x0y1falseif_minsort3trueadd2nxyapp2rm2nxyfalseapp'app1x0y1app2x0y1falseeq2s1xs1yeq2xytrueeq2s1xs1yeq2xy1true12true2le2s1xs1yle2xytruele2s1xs1yle2xy1true12true2app2add2nxyapp2xytrueapp2add2nxyapp2xy1true12false2AProVEAProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Statistics for single proof: 100.00 % (27 real / 0 unknown / 0 assumptions / 27 total proof steps)http://aprove.informatik.rwth-aachen.deJohnDoe