reserve S for non empty non void ManySortedSign,
  A for MSAlgebra over S;
reserve A for non-empty MSAlgebra over S;

theorem Th19:
  for s1,s2,s3 being SortSymbol of S st TranslationRel S reduces
  s1,s2 for t being Translation of A,s1,s2 for f being Function st f
  is_e.translation_of A,s2,s3 holds f*t is Translation of A,s1,s3
proof
  let s1,s2,s3 be SortSymbol of S such that
A1: TranslationRel S reduces s1,s2;
  let t be Translation of A,s1,s2;
  let f be Function;
  assume
A2: f is_e.translation_of A,s2,s3;
  then
A3: f is Translation of A,s2,s3 by Th17;
  TranslationRel S reduces s2,s3 by A2,Th17;
  hence thesis by A1,A3,Th18;
end;
