theorem
  for A being disjoint_valued non-empty MSAlgebra over S
  for B being non-empty MSAlgebra over S
  for f being ManySortedFunction of A,B
  for a being Element of (the Sorts of A).s holds
  f.a is Element of (the Sorts of B).s
  proof
    let A be disjoint_valued non-empty MSAlgebra over S;
    let B be non-empty MSAlgebra over S;
    let f be ManySortedFunction of A,B;
    let a be Element of (the Sorts of A).s;
    f.a = f.s.a in (the Sorts of B).s by Th9,FUNCT_2:5;
    hence thesis;
  end;
