reserve x,y,z,r,s for ExtReal;
reserve A,B for ext-real-membered set;

theorem
  for X,Y being ext-real-membered set holds max(inf X,inf Y) <= inf(X /\ Y)
proof
  let X,Y be ext-real-membered set;
A1: inf Y is LowerBound of Y by Def4;
  inf X is LowerBound of X by Def4;
  then max(inf X,inf Y) is LowerBound of X /\ Y by A1,Th66;
  hence thesis by Def4;
end;
