% Mizar problem: t193_orders_1,orders_1,2238,20 
fof(t193_orders_1,conjecture,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : k4_relat_1(k2_wellord1(A,B)) = k2_wellord1(k4_relat_1(A),B) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k3_xboole_0,idempotence_k3_xboole_0,dt_k2_zfmisc_1,dt_k3_xboole_0,involutiveness_k4_relat_1,dt_k2_wellord1,dt_k4_relat_1,d6_wellord1,l171_orders_1]),
    [file(orders_1,t193_orders_1)]).

fof(commutativity_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ),
    file(xboole_0,k3_xboole_0),
    []).

fof(idempotence_k3_xboole_0,axiom,(
    ! [A,B] : k3_xboole_0(A,A) = A ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

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(dt_k2_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k2_wellord1(A,B)) ) ),
    file(wellord1,k2_wellord1),
    []).

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(d6_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : k2_wellord1(A,B) = k3_xboole_0(A,k2_zfmisc_1(B,B)) ) ),
    file(wellord1,d6_wellord1),
    []).

fof(l171_orders_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : k4_relat_1(k2_wellord1(A,B)) = k2_wellord1(k4_relat_1(A),B) ) ),
    file(orders_1,l171_orders_1),
    []).