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 Th22:
  G1 c= G & G2 c= G implies (G1 \/ G2) c= G
proof
  assume
A1: G1 c= G & G2 c= G;
  then A2: (
the Source of G1) c= (the Source of G) & (the Source of G2) c= (the Source
  of G) by Th5;
  A3: (
the Target of G1) c= (the Target of G) & (the Target of G2) c= (the Target
  of G) by A1,Th5;
A4: (the Source of G1) tolerates (the Source of G2) by A2,PARTFUN1:57;
 (the Target of G1) tolerates (the Target of G2) by A3,PARTFUN1:57;
then  (G1 \/ G2) is_sum_of G1, G2 by A4;
  hence thesis by A1,Th21;
end;
