reserve x, y, z, v for set,
  n, m, k for Nat;
reserve G, G1, G2, G3 for Graph;
reserve x, y for Element of (the carrier of G);

theorem
  G1 in bool G & G2 in bool G implies (G1 \/ G2) in bool G
proof
  assume that
A1: G1 in bool G and
A2: G2 in bool G;
A3: G1 is Subgraph of G by A1,Def25;
A4: G2 is Subgraph of G by A2,Def25;
A5: G1 c= G by A3;
 G2 c= G by A4;
then  (G1 \/ G2) c= G by A5,Th22;
then  (G1 \/ G2) is Subgraph of G;
  hence thesis by Def25;
end;
