
theorem
  for F being non empty Graph-yielding Function, S being GraphSum of F
  holds card F c= S.numComponents()
proof
  let F be non empty Graph-yielding Function, S be GraphSum of F;
  consider G9 being GraphUnion of rng canGFDistinction(F) such that
    A1: S is G9-Disomorphic by Def27;
  consider H being PGraphMapping of G9, S such that
    A2: H is Disomorphism by A1, GLIB_010:def 24;
  A3: card F = card dom F by CARD_1:62
    .= card dom canGFDistinction(F) by Def25
    .= card rng canGFDistinction(F) by CARD_1:70;
  S.numComponents() = G9.numComponents() by A2, GLIBPRE1:83;
  hence thesis by A3, Th68;
end;
