reserve x,y for object,X,Y for set;
reserve M for Pnet;

theorem Th11:
  ((Flow M)|(the carrier' of M)) * ((Flow M)|(the carrier' of M)) = {} &
  ((Flow M)~|(the carrier' of M)) *
  ((Flow M)~|(the carrier' of M)) = {} &
  ((Flow M)|(the carrier' of M)) *
  ((Flow M)~|(the carrier' of M)) = {} &
  ((Flow M)~|(the carrier' of M)) *
  ((Flow M)|(the carrier' of M)) = {} &
  ((Flow M)|(the carrier of M)) *
  ((Flow M)|(the carrier of M)) = {} &
  ((Flow M)~|(the carrier of M)) *
  ((Flow M)~|(the carrier of M)) = {} &
  ((Flow M)|(the carrier of M)) *
  ((Flow M)~|(the carrier of M)) = {} &
  ((Flow M)~|(the carrier of M)) *
  ((Flow M)|(the carrier of M)) = {}
proof
A1: rng ((Flow M)|(the carrier' of M)) misses
  dom ((Flow M)|(the carrier' of M)) by Th10;
A2: rng ((Flow M)~|(the carrier' of M)) misses
  dom ((Flow M)~|(the carrier' of M)) by Th10;
A3: rng ((Flow M)|(the carrier' of M)) misses
  dom ((Flow M)~|(the carrier' of M)) by Th10;
A4: rng ((Flow M)~|(the carrier' of M)) misses
  dom ((Flow M)|(the carrier' of M)) by Th10;
A5: rng ((Flow M)|(the carrier of M)) misses
  dom ((Flow M)|(the carrier of M)) by Th10;
A6: rng ((Flow M)~|(the carrier of M)) misses
  dom ((Flow M)~|(the carrier of M)) by Th10;
A7: rng ((Flow M)|(the carrier of M)) misses
  dom ((Flow M)~|(the carrier of M)) by Th10;
  rng ((Flow M)~|(the carrier of M)) misses
  dom ((Flow M)|(the carrier of M)) by Th10;
  hence thesis by A1,A2,A3,A4,A5,A6,A7,RELAT_1:44;
end;
