% Mizar problem: t128_relat_1,relat_1,1805,17 
fof(t128_relat_1,conjecture,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => k8_relat_1(A,k8_relat_1(A,B)) = k8_relat_1(A,B) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k3_xboole_0,dt_k3_xboole_0,dt_k8_relat_1,fc1_relat_1,idempotence_k3_xboole_0,t127_relat_1]),
    [file(relat_1,t128_relat_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(dt_k3_xboole_0,axiom,(
    $true ),
    file(xboole_0,k3_xboole_0),
    []).

fof(dt_k8_relat_1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => v1_relat_1(k8_relat_1(A,B)) ) ),
    file(relat_1,k8_relat_1),
    []).

fof(fc1_relat_1,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_relat_1(B) )
     => v1_relat_1(k3_xboole_0(A,B)) ) ),
    file(relat_1,fc1_relat_1),
    []).

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

fof(t127_relat_1,axiom,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => k8_relat_1(A,k8_relat_1(B,C)) = k8_relat_1(k3_xboole_0(A,B),C) ) ),
    file(relat_1,t127_relat_1),
    []).