reserve a,b,c,d for Real;
reserve r,s for Real;

theorem
  r < s implies r < (r+s)/2 & (r+s)/2 < s
proof
  assume r < s;
  then
A1: r/2 < s/2 by Lm26;
  then r/2 + r/2 < r/2 + s/2 by Lm10;
  hence r < (r+s)/2;
  r/2 + s/2 < s/2 + s/2 by A1,Lm10;
  hence thesis;
end;
