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 Th19:
  (the Source of G1) tolerates (the Source of G2) &
  (the Target of G1) tolerates (the Target of G2) implies
  G1 c= G1 \/ G2 & G2 c= G1 \/ G2
proof
  assume (the Source of G1) tolerates (the Source of G2) & (the Target of G1)
  tolerates (the Target of G2);
then  (G1 \/ G2) is_sum_of G1, G2;
  hence thesis by Th18;
end;
