reserve i,j,n,k,m for Nat,
     a,b,x,y,z for object,
     F,G for FinSequence-yielding FinSequence,
     f,g,p,q for FinSequence,
     X,Y for set,
     D for non empty set;

theorem Th49:
  for P,S be FinSequence-membered set st
    P c= doms F & S c= doms G holds P^S c= doms (F^G)
proof
  let P,S be FinSequence-membered set such that
A1: P c= doms F & S c= doms G;
  let x such that
A2: x in P^S;
  ex p,s be FinSequence st x=p^s & p in P & s in S by A2,POLNOT_1:def 2;
  hence thesis by A1,Th48;
end;
