
theorem Th25:
  for R being right_unital non empty multLoopStr, A being non
  empty Subset of R, f being LeftLinearCombination of A holds f is
  LinearCombination of A
proof
  let R be right_unital non empty multLoopStr, A be non empty Subset of R, f
  be LeftLinearCombination 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 = r*a by Def9;
  f/.i = r*a*1.R by A1;
  hence thesis;
end;
