
theorem Th2:
  for S being non empty non void ManySortedSign
  for A being MSAlgebra over S
  for B being MSSubAlgebra of A
  for s being SortSymbol of S
  for a being set st a in (the Sorts of B).s
  holds a in (the Sorts of A).s
  proof
    let S be non empty non void ManySortedSign;
    let A be MSAlgebra over S;
    let B be MSSubAlgebra of A;
    let s be SortSymbol of S;
    the Sorts of B is MSSubset of A by MSUALG_2:def 9;
    then (the Sorts of B).s c= (the Sorts of A).s by PBOOLE:def 18,def 2;
    hence thesis;
  end;
