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 Th12:
  (ex G st G1 c= G & G2 c= G) implies G1 \/ G2 = G2 \/ G1
proof
  given G such that
A1: G1 c= G & G2 c= G;
  A2: ( the Source of G1) c= (the Source of G) & ( the Source of G2) c= (the
  Source of G) by A1,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,PARTFUN1:52;
 (the Target of G1) tolerates (the Target of G2) by A3,PARTFUN1:52;
  hence thesis by A4,Th8;
end;
