theorem Th25:
  the_arity_of o1 <= the_arity_of o2 implies Args(o1,A) c= Args(o2 ,A)
proof
  reconsider M = the Sorts of A as OrderSortedSet of S by Th17;
A1: M#.(the_arity_of o1) = M#.((the Arity of S).o1) by MSUALG_1:def 1
    .= (M# * (the Arity of S)).o1 by FUNCT_2:15
    .= Args(o1,A) by MSUALG_1:def 4;
A2: M#.(the_arity_of o2) = M#.((the Arity of S).o2) by MSUALG_1:def 1
    .= (M# * (the Arity of S)).o2 by FUNCT_2:15
    .= Args(o2,A) by MSUALG_1:def 4;
  assume the_arity_of o1 <= the_arity_of o2;
  hence thesis by A1,A2,Th20;
end;
