theorem
  LSeg(E-min X, E-max X) c= LSeg(SE-corner X, NE-corner X)
proof
A1: (SE-corner X)`1 = E-bound X & (NE-corner X)`1 = E-bound X by EUCLID:52;
A2: (E-max X)`2 <= (NE-corner X)`2 by Th46;
  (E-max X)`1 = E-bound X & (SE-corner X)`2 <= (E-max X)`2 by Th46,EUCLID:52;
  then
A3: E-max X in LSeg(SE-corner X, NE-corner X) by A1,A2,GOBOARD7:7;
A4: (E-min X)`2 <= (NE-corner X)`2 by Th46;
  (E-min X)`1 = E-bound X & (SE-corner X)`2 <= (E-min X)`2 by Th46,EUCLID:52;
  then E-min X in LSeg(SE-corner X, NE-corner X) by A1,A4,GOBOARD7:7;
  hence thesis by A3,TOPREAL1:6;
end;
