appappminusx0xappappminusappsxappsyappappminusxyappf0apps0appfappsxappappminusappsxappgappfxappg00appgappsxappappminusappsxappfappgxappappmapfunnilnilappappmapfunappappconsxxsappappconsappfunxappappmapfunxsappappfilterfunnilnilappappfilterfunappappconsxxsappappappappfilter2appfunxfunxxsappappappappfilter2truefunxxsappappconsxappappfilterfunxsappappappappfilter2falsefunxxsappappfilterfunxs2.1appminus0minusminus1minus2000s0ss1f0ff1g0gg1map0mapmap1map2nil0nilcons0conscons1cons2filter0filterfilter1filter3filter20filter2filter21filter22filter23filter24true0truefalse0falseappminusy1minus1y1appminus1x0y1minus2x0y1appsy1s1y1appfy1f1y1appgy1g1y1appmapy1map1y1appmap1x0y1map2x0y1appconsy1cons1y1appcons1x0y1cons2x0y1appfiltery1filter1y1appfilter1x0y1filter3x0y1appfilter2y1filter21y1appfilter21x0y1filter22x0y1appfilter22x0x1y1filter23x0x1y1appfilter23x0x1x2y1filter24x0x1x2y1minus2x0xminus2s1xs1yminus2xyf10s10f1s1xminus2s1xg1f1xg100g1s1xminus2s1xf1g1xmap2funnilnilmap2funcons2xxscons2appfunxmap2funxsfilter3funnilnilfilter3funcons2xxsfilter24appfunxfunxxsfilter24truefunxxscons2xfilter3funxsfilter24falsefunxxsfilter3funxsappminusy1minus1y1appminus1x0y1minus2x0y1appsy1s1y1appfy1f1y1appgy1g1y1appmapy1map1y1appmap1x0y1map2x0y1appconsy1cons1y1appcons1x0y1cons2x0y1appfiltery1filter1y1appfilter1x0y1filter3x0y1appfilter2y1filter21y1appfilter21x0y1filter22x0y1appfilter22x0x1y1filter23x0x1y1appfilter23x0x1x2y1filter24x0x1x2y110minus2s1xs1yminus2xyf1s1xminus2s1xg1f1xf1s1xg1f1xf1s1xf1xg1s1xminus2s1xf1g1xg1s1xf1g1xg1s1xg1xmap2funcons2xxsappfunxmap2funcons2xxsmap2funxsfilter3funcons2xxsfilter24appfunxfunxxsfilter3funcons2xxsappfunxfilter24truefunxxsfilter3funxsfilter24falsefunxxsfilter3funxsappminus1x0y1minus2x0y1appfy1f1y1appgy1g1y1appmap1x0y1map2x0y1appfilter1x0y1filter3x0y1appfilter23x0x1x2y1filter24x0x1x2y1trueappmap1x0y1map2x0y1map2funcons2xxsappfunxappfilter1x0y1filter3x0y1filter3funcons2xxsfilter24appfunxfunxxsfilter24truefunxxsfilter3funxsfilter3funcons2xxsappfunxappfilter23x0x1x2y1filter24x0x1x2y1filter24falsefunxxsfilter3funxsmap2funcons2xxsmap2funxstruemap2funcons2xxsappfunx1false12true2map2funcons2xxsmap2funxs1false12true2filter3funcons2xxsappfunx1false12true2appmap1x0y1map2x0y11true12false2filter3funcons2xxsfilter24appfunxfunxxs1false22true32true4appfilter1x0y1filter3x0y11true12false2appfilter23x0x1x2y1filter24x0x1x2y11true11true21true32false4filter24truefunxxsfilter3funxs2false14false2filter24falsefunxxsfilter3funxs2false14false2appfy1f1y1falseappgy1g1y1falsef1s1xg1f1xg1s1xf1g1xf1s1xf1xg1s1xg1xtrueg100g1s1xminus2s1xf1g1xf10s10f1s1xminus2s1xg1f1xminus2x0xminus2s1xs1yminus2xyminus2x00minus2s1x0s1x1f10f1s1x0g10g1s1x0f111s110g111f110g110002minus220f111s111g111f111g11100minus221f1s1xg1f1xg1s1xf1g1xf111s111g110f111001f111s111g111f111g11100minus221f1s1xminus2s1xg1f1xfalseg1s1xminus2s1xf1g1xfalseappminus1x0y1minus2x0y1falseminus2s1xs1yminus2xytrueminus2s1xs1yminus2xy1true12true2AProVEAProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Statistics for single proof: 100.00 % (13 real / 0 unknown / 0 assumptions / 13 total proof steps)http://aprove.informatik.rwth-aachen.deJohnDoe