reserve x for set;
reserve a,b,c,d for ExtReal;

theorem
  a < b & c < d implies max(a,c) < max(b,d)
proof
  assume that
A1: a < b and
A2: c < d;
  d <= max(b,d) by Th25;
  then
A3: c < max(b,d) by A2,Th2;
  b <= max(b,d) by Th25;
  then a < max(b,d) by A1,Th2;
  hence thesis by A3,Def9;
end;
