let H be removeParallelEdges of G; :: thesis: not H is loopless
consider E being RepEdgeSelection of G such that
A1: H is inducedSubgraph of G, the_Vertices_of G,E by GLIB_009:def 7;
consider v being object such that
A2: ex e being object st e Joins v,v,G by GLIB_000:18;
consider e0 being object such that
A3: e0 Joins v,v,G by A2;
consider e being object such that
A4: ( e Joins v,v,G & e in E ) and
for e9 being object st e9 Joins v,v,G & e9 in E holds
e9 = e by A3, GLIB_009:def 5;
A5: the_Edges_of G = G .edgesBetween (the_Vertices_of G) by GLIB_000:34;
the_Vertices_of G c= the_Vertices_of G ;
then A6: e in the_Edges_of H by A1, A4, A5, GLIB_000:def 37;
( v is set & e is set ) by TARSKI:1;
then e Joins v,v,H by A4, A6, GLIB_000:73;
hence not H is loopless by GLIB_000:18; :: thesis: verum