reserve D for non empty set,
  i,j,k,l for Nat,
  n for Nat,
  x for set,
  a,b,c,r,r1,r2 for Real,
  p,q for FinSequence of REAL,
  MR,MR1 for Matrix of REAL;

theorem Th15:
  for p being ProbFinS FinSequence of REAL for k st k in dom p & p
  .k = 1 holds p has_onlyone_value_in k
proof
  let p be ProbFinS FinSequence of REAL;
  let k such that
A1: k in dom p and
A2: p.k = 1;
  p.k = Sum p by A2,MATRPROB:def 5;
  hence thesis by A1,Th14;
end;
