theorem Th55:
  p`2 <= q`2 implies S-bound LSeg(p,q) = p`2
proof
  assume
A1: p`2 <= q`2;
  then
A2: proj2.:LSeg(p,q) = [.p`2,q`2.] by Th53;
  thus S-bound LSeg(p,q) = lower_bound(proj2.:LSeg(p,q)) by Th44
    .= p`2 by A1,A2,JORDAN5A:19;
end;
