
theorem Th28:
  for R being left_unital non empty multLoopStr, A being non
  empty Subset of R, f being RightLinearCombination of A holds
  f is LinearCombination of A
proof
  let R be left_unital non empty multLoopStr, A be non empty Subset of R, f
  be RightLinearCombination of A;
  let i be set;
  assume i in dom f;
  then consider r being Element of R, a being Element of A such that
A1: f/.i = a*r by Def10;
  f/.i = 1.R*a*r by A1;
  hence thesis;
end;
