
theorem Th35:
  for L being RelStr, X,Y being set st X c= Y & ex_inf_of X,L &
  ex_inf_of Y,L holds "/\"(X,L) >= "/\"(Y,L)
proof
  let L be RelStr, X,Y be set;
  assume that
A1: X c= Y and
A2: ex_inf_of X,L and
A3: ex_inf_of Y,L;
  "/\"(Y,L) is_<=_than X
  proof
    let x be Element of L;
    assume
A4: x in X;
    "/\"(Y,L) is_<=_than Y by A3,Def10;
    hence thesis by A1,A4;
  end;
  hence thesis by A2,Def10;
end;
