reserve a,b,r,x,y for Real,
  i,j,k,n for Nat,
  x1 for set;

theorem
  for p be non-decreasing real-valued FinSequence, i,j st
  i in dom p & j in dom p & i <= j holds p.i <= p.j
proof
  let p be non-decreasing real-valued FinSequence;
  for n be Nat st n in dom p & n+1 in dom p holds p.n <= p.(n+1) by Def1;
  hence thesis by LM;
end;
