% Mizar problem: t40_wellord1,wellord1,680,63 
fof(t40_wellord1,conjecture,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( v2_wellord1(B)
       => k3_relat_1(k2_wellord1(B,k1_wellord1(B,A))) = k1_wellord1(B,A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,commutativity_k3_xboole_0,d6_relat_1,d6_wellord1,dt_k1_relat_1,dt_k1_wellord1,dt_k1_zfmisc_1,dt_k2_relat_1,dt_k2_wellord1,dt_k2_xboole_0,dt_k2_zfmisc_1,dt_k3_relat_1,dt_k3_xboole_0,dt_m1_subset_1,existence_m1_subset_1,idempotence_k2_xboole_0,idempotence_k3_xboole_0,reflexivity_r1_tarski,t13_wellord1,t39_wellord1,t3_subset]),
    [file(wellord1,t40_wellord1)]).

fof(commutativity_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) ),
    file(xboole_0,k2_xboole_0),
    []).

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(d6_relat_1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => k3_relat_1(A) = k2_xboole_0(k1_relat_1(A),k2_relat_1(A)) ) ),
    file(relat_1,d6_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(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k1_wellord1,axiom,(
    $true ),
    file(wellord1,k1_wellord1),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_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_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(dt_k3_relat_1,axiom,(
    $true ),
    file(relat_1,k3_relat_1),
    []).

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

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(idempotence_k2_xboole_0,axiom,(
    ! [A,B] : k2_xboole_0(A,A) = A ),
    file(xboole_0,k2_xboole_0),
    []).

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

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t13_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k1_wellord1(B,A),k3_relat_1(B)) ) ),
    file(wellord1,t13_wellord1),
    []).

fof(t39_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( ( v2_wellord1(B)
          & r1_tarski(A,k3_relat_1(B)) )
       => k3_relat_1(k2_wellord1(B,A)) = A ) ) ),
    file(wellord1,t39_wellord1),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).