theorem Th22:
  for S being non empty non void ManySortedSign
  for a being SortSymbol of S
  for o being OperSymbol of S st the_arity_of o = <*a*>
  for A being MSAlgebra over S holds
  Args(o,A) = product <*(the Sorts of A).a*>
  proof
    let S be non empty non void ManySortedSign;
    let a be SortSymbol of S;
    let o be OperSymbol of S;
    assume A1: the_arity_of o = <*a*>;
    let A be MSAlgebra over S;
A2: dom the Sorts of A = the carrier of S by PARTFUN1:def 2;
    thus Args(o,A) = product ((the Sorts of A)*the_arity_of o) by PRALG_2:3
    .= product <*(the Sorts of A).a*> by A1,A2,FINSEQ_2:34;
  end;
