theorem Th41:
  dom f = dom ((repeat(Relax(n)*findmin(n))).i.f)
proof
  set R=Relax(n), M=findmin(n);
  defpred P[Nat] means dom f = dom ((repeat(R*M)).$1.f);
  dom ((repeat(R*M)).0 .f)= dom ((id (REAL*)).f) by Def2
    .= dom f;
  then
A1: P[0];
A2: for k st P[k] holds P[k+1] by Th37;
  for k holds P[k] from NAT_1:sch 2(A1,A2);
  hence thesis;
end;
