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

theorem Th26:
  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;
