% Mizar problem: t8_wellord1,wellord1,153,49 
fof(t8_wellord1,conjecture,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( r2_wellord1(A,k3_relat_1(A))
      <=> v2_wellord1(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xboole_0,d12_relat_2,d14_relat_2,d16_relat_2,d4_wellord1,d5_wellord1,d6_relat_1,d9_relat_2,dt_k1_relat_1,dt_k2_relat_1,dt_k2_xboole_0,dt_k3_relat_1,idempotence_k2_xboole_0,t5_wellord1]),
    [file(wellord1,t8_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(d12_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v4_relat_2(A)
      <=> r4_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d12_relat_2),
    []).

fof(d14_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v6_relat_2(A)
      <=> r6_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d14_relat_2),
    []).

fof(d16_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v8_relat_2(A)
      <=> r8_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d16_relat_2),
    []).

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(d5_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r2_wellord1(A,B)
        <=> ( r1_relat_2(A,B)
            & r8_relat_2(A,B)
            & r4_relat_2(A,B)
            & r6_relat_2(A,B)
            & r1_wellord1(A,B) ) ) ) ),
    file(wellord1,d5_wellord1),
    []).

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(d9_relat_2,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_relat_2(A)
      <=> r1_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d9_relat_2),
    []).

fof(dt_k1_relat_1,axiom,(
    $true ),
    file(relat_1,k1_relat_1),
    []).

fof(dt_k2_relat_1,axiom,(
    $true ),
    file(relat_1,k2_relat_1),
    []).

fof(dt_k2_xboole_0,axiom,(
    $true ),
    file(xboole_0,k2_xboole_0),
    []).

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

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

fof(t5_wellord1,axiom,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_wellord1(A)
      <=> r1_wellord1(A,k3_relat_1(A)) ) ) ),
    file(wellord1,t5_wellord1),
    []).