reserve A,B,C,Y,x,y,z for set, U, D for non empty set,
X for non empty Subset of D, d,d1,d2 for Element of D;
reserve P,Q,R for Relation, g for Function, p,q for FinSequence;
reserve f for BinOp of D, i,m,n for Nat;

theorem Th4: for x,y being FinSequence st x is U-valued & y is U-valued
holds (U-concatenation).(x,y)=x^y
proof
let x,y be FinSequence; set f=U-concatenation; assume x is U-valued &
y is U-valued; then reconsider xx=x, yy=y as FinSequence of U by Lm1;
f.(xx,yy)=xx^yy by Lm10; hence thesis;
end;
