% Mizar ND problem: t189_orders_1,orders_1,2226,36 
fof(involutiveness_k4_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => k4_relat_1(k4_relat_1(A)) = A ) ),
    file(relat_1,k4_relat_1),
    [interesting(0.9),axiom,file(relat_1,k4_relat_1)]).

fof(dt_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => v1_relat_1(k4_relat_1(A)) ) ),
    file(relat_1,k4_relat_1),
    [interesting(0.9),axiom,file(relat_1,k4_relat_1)]).

fof(l154_orders_1,plain,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_relat_2(A,B)
         => r1_relat_2(k4_relat_1(A),B) ) ) ),
    file(orders_1,l154_orders_1),
    [interesting(0.9),axiom,file(orders_1,l154_orders_1)]).

fof(t189_orders_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_relat_2(A,B)
         => r1_relat_2(k4_relat_1(A),B) ) ) ),
    inference(mizar_by,[status(thm),assumptions([])],[involutiveness_k4_relat_1,dt_k4_relat_1,l154_orders_1]),
    [interesting(1),file(orders_1,t189_orders_1),[file(orders_1,t189_orders_1)]]).