reserve X for set, x,y,z for object,
  k,l,n for Nat,
  r for Real;
reserve i,i0,i1,i2,i3,i4,i5,i8,i9,j for Integer;
reserve r1,p,p1,g,g1,g2 for Real,
  Y for Subset of REAL;

theorem Th50:
  for a,b being Integer st a < b holds a <= b - 1
proof
  let a,b be Integer;
  assume a < b;
  then a - 1 < b - 1 by XREAL_1:9;
  then a - 1 + 1 <= b - 1 by Th7;
  hence thesis;
end;
