reserve k, m, n, p, K, N for Nat;
reserve i for Integer;
reserve x, y, eps for Real;
reserve seq, seq1, seq2 for Real_Sequence;
reserve sq for FinSequence of REAL;

theorem Th40:
  for n be Real st n>=2 & x=1/(n+1) holds x/(1-x)<1
proof
  let n be Real;
  assume that
A1: n>=2 and
A2: x=1/(n+1);
  n+1 > n by XREAL_1:29;
  then 2<n+1 by A1,XXREAL_0:2;
  then 2/(n+1)<1 by XREAL_1:189;
  then x+x<1 by A2;
  then x<1-x by XREAL_1:20;
  hence thesis by A1,A2,XREAL_1:189;
end;
