% Mizar problem: t137_orders_1,orders_1,759,32 
fof(t137_orders_1,conjecture,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r2_orders_1(A,B)
         => r2_orders_1(k4_relat_1(A),B) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d7_orders_1,dt_k4_relat_1,involutiveness_k4_relat_1,l154_orders_1,l155_orders_1,l156_orders_1]),
    [file(orders_1,t137_orders_1)]).

fof(d7_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r2_orders_1(A,B)
        <=> ( r1_relat_2(A,B)
            & r8_relat_2(A,B)
            & r4_relat_2(A,B) ) ) ) ),
    file(orders_1,d7_orders_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),
    []).

fof(involutiveness_k4_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k4_relat_1(k4_relat_1(A)) = A ) ),
    file(relat_1,k4_relat_1),
    []).

fof(l154_orders_1,axiom,(
    ! [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),
    []).

fof(l155_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r8_relat_2(A,B)
         => r8_relat_2(k4_relat_1(A),B) ) ) ),
    file(orders_1,l155_orders_1),
    []).

fof(l156_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r4_relat_2(A,B)
         => r4_relat_2(k4_relat_1(A),B) ) ) ),
    file(orders_1,l156_orders_1),
    []).