reserve GS for GraphStruct;
reserve G,G1,G2,G3 for _Graph;
reserve e,x,x1,x2,y,y1,y2,E,V,X,Y for set;
reserve n,n1,n2 for Nat;
reserve v,v1,v2 for Vertex of G;

theorem
  for G1 being _finite _Graph, E being Subset of the_Edges_of G1, G2
  being removeEdges of G1,E holds G2.size() + card E = G1.size()
proof
  let G1 be _finite _Graph, E be Subset of the_Edges_of G1, G2 be removeEdges
  of G1,E;
A1: the_Edges_of G2 = the_Edges_of G1 \ E by Th53;
  then the_Edges_of G1 = the_Edges_of G2 \/ E by XBOOLE_1:45;
  hence thesis by A1,CARD_2:40,XBOOLE_1:79;
end;
