reserve f for Function;
reserve p,q for FinSequence;
reserve A,B,C for set,x,x1,x2,y,z for object;
reserve k,l,m,n for Nat;
reserve a for Nat;
reserve D for non empty set;
reserve d,d1,d2,d3 for Element of D;

theorem Th27:
  x in rng p & (for k st k in dom p & k <> x..p holds p.k <> x)
  implies p just_once_values x
proof
  assume that
A1: x in rng p and
A2: for k st k in dom p & k <> x..p holds p.k <> x;
A3: for z being object st z in dom p & z <> x..p holds p.z <> x by A2;
  p.(x..p) = x & x..p in dom p by A1,Th19,Th20;
  hence thesis by A3,Th7;
end;
