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

theorem Th5:
  a < b implies ex c st a < c & c < b
proof
  assume
A1: a < b;
  take z = (a+b)/2;
  1*a+a < a+b by A1,Lm10;
  then 2"*(2*a) < 2"*(a+b) by Lm13;
  hence a < z;
  a+b < 1*b+b by A1,Lm10;
  then 2"*(a+b) < 2"*(2*b) by Lm13;
  hence thesis;
end;
