let G1 be loopless _Graph; :: thesis: for G2 being _Graph holds
( G1 == G2 iff G2 is removeLoops of G1 )
let G2 be _Graph; :: thesis: ( G1 == G2 iff G2 is removeLoops of G1 )

hereby :: thesis: ( G2 is removeLoops of G1 implies G1 == G2 )

assume A1: G1 == G2 ; :: thesis: G2 is removeLoops of G1
G1 is inducedSubgraph of G1,(the_Vertices_of G1) by GLIB_000:100;
then G1 is inducedSubgraph of G1, the_Vertices_of G1, the_Edges_of G1 by GLIB_000:34;
hence G2 is removeLoops of G1 by A1, GLIB_000:101; :: thesis: verum

end;

assume G2 is removeLoops of G1 ; :: thesis: G1 == G2
then G2 is inducedSubgraph of G1,(the_Vertices_of G1) by GLIB_000:34;
hence G1 == G2 by GLIB_000:94; :: thesis: verum