reserve X for non empty set,
        x for Element of X,
        S for SigmaField of X,
        M for sigma_Measure of S,
        f,g,f1,g1 for PartFunc of X,REAL,
        l,m,n,n1,n2 for Nat,
        a,b,c for Real;
reserve k for positive Real;

theorem Th8:
f to_power 1 = f
proof
A1:dom (f to_power 1) = dom f by MESFUN6C:def 4;
   for x be object st x in dom (f to_power 1) holds (f to_power 1).x = f.x
   proof
    let x be object;
    assume x in dom(f to_power 1); then
    (f to_power 1).x = (f.x) to_power 1 by MESFUN6C:def 4;
    hence thesis by POWER:25;
   end;
   hence thesis by A1,FUNCT_1:2;
end;
