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;

theorem
  f is_one-to-one_at x implies f <- (f.x) = x
proof
  assume f is_one-to-one_at x;
  then x in dom f & f just_once_values f.x by Th9;
  hence thesis by Def3;
end;
