% Mizar problem: t32_wellord1,wellord1,473,58 
fof(t32_wellord1,conjecture,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( v2_wellord1(B)
       => v2_wellord1(k2_wellord1(B,A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k3_xboole_0,d4_wellord1,d6_wellord1,dt_k2_wellord1,dt_k2_zfmisc_1,dt_k3_xboole_0,idempotence_k3_xboole_0,t22_wellord1,t23_wellord1,t24_wellord1,t25_wellord1,t31_wellord1]),
    [file(wellord1,t32_wellord1)]).

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(d4_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_wellord1(A)
      <=> ( v1_relat_2(A)
          & v8_relat_2(A)
          & v4_relat_2(A)
          & v6_relat_2(A)
          & v1_wellord1(A) ) ) ) ),
    file(wellord1,d4_wellord1),
    []).

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_k2_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(A)
     => v1_relat_1(k2_wellord1(A,B)) ) ),
    file(wellord1,k2_wellord1),
    []).

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

fof(t22_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( v1_relat_2(B)
       => v1_relat_2(k2_wellord1(B,A)) ) ) ),
    file(wellord1,t22_wellord1),
    []).

fof(t23_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( v6_relat_2(B)
       => v6_relat_2(k2_wellord1(B,A)) ) ) ),
    file(wellord1,t23_wellord1),
    []).

fof(t24_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( v8_relat_2(B)
       => v8_relat_2(k2_wellord1(B,A)) ) ) ),
    file(wellord1,t24_wellord1),
    []).

fof(t25_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( v4_relat_2(B)
       => v4_relat_2(k2_wellord1(B,A)) ) ) ),
    file(wellord1,t25_wellord1),
    []).

fof(t31_wellord1,axiom,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( v1_wellord1(B)
       => v1_wellord1(k2_wellord1(B,A)) ) ) ),
    file(wellord1,t31_wellord1),
    []).