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

theorem
  a < b & c < d implies min(a,c) < min(b,d)
proof
  assume that
A1: a < b and
A2: c < d;
  min(a,c) <= c by Th17;
  then
A3: min(a,c) < d by A2,Th2;
  min(a,c) <= a by Th17;
  then min(a,c) < b by A1,Th2;
  hence thesis by A3,Def8;
end;
