
theorem Th10:
  for G being _finite real-weighted WGraph, EL being FF:ELabeling
  of G, source being Vertex of G holds source in dom AP:FindAugPath(EL,source)
proof
  let G be _finite real-weighted WGraph, EL being FF:ELabeling of G, source be
  Vertex of G;
  set CS = AP:CompSeq(EL,source);
  dom (CS.0) = {source} by Th4;
  then
A1: source in dom (CS.0) by TARSKI:def 1;
  dom (CS.0) c= dom AP:FindAugPath(EL,source) by Th5;
  hence thesis by A1;
end;
