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

theorem Th15:
  a <= b & c < d implies a-d < b-c
proof
  assume
A1: a <= b;
  assume c < d;
  then -d < -c by Lm15;
  then a+-d < b+-c by A1,Lm8;
  hence thesis;
end;
