% Mizar problem: t13_conmetr1,conmetr1,1611,50 
fof(t13_conmetr1,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v3_conmetr1(k3_analmetr(A))
      <=> v6_conmetr(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_analoaf,antisymmetry_r2_hidden,cc1_analmetr,d3_conmetr1,d6_conmetr,dt_g1_analoaf,dt_k1_zfmisc_1,dt_k2_zfmisc_1,dt_k3_analmetr,dt_l1_analmetr,dt_l1_analoaf,dt_l1_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_analoaf,dt_u1_struct_0,existence_l1_analmetr,existence_l1_analoaf,existence_l1_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc2_analmetr,fc3_analmetr,fc4_analmetr,free_g1_analoaf,rc2_analmetr,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t3_subset,t47_analmetr,t48_analmetr,t4_subset,t57_analmetr,t58_analmetr]),
    [file(conmetr1,t13_conmetr1)]).

fof(abstractness_v1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => ( v1_analoaf(A)
       => A = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) ) ),
    file(analoaf,v1_analoaf),
    []).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_analmetr,axiom,(
    ! [A] : 
      ( l1_analmetr(A)
     => ( ( ~ v3_struct_0(A)
          & v3_analmetr(A) )
       => ( ~ v3_struct_0(A)
          & v2_analmetr(A) ) ) ) ),
    file(analmetr,cc1_analmetr),
    []).

fof(d3_conmetr1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v3_conmetr1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A)))
                                           => ! [K] : 
                                                ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A)))
                                               => ( ( v1_aff_1(J,A)
                                                    & v1_aff_1(K,A)
                                                    & r2_hidden(B,J)
                                                    & r2_hidden(D,J)
                                                    & r2_hidden(F,J)
                                                    & r2_hidden(H,J)
                                                    & r2_hidden(C,K)
                                                    & r2_hidden(E,K)
                                                    & r2_hidden(G,K)
                                                    & r2_hidden(I,K)
                                                    & r2_analoaf(A,D,C,H,G)
                                                    & r2_analoaf(A,C,B,G,F)
                                                    & r2_analoaf(A,B,E,F,I) )
                                                 => ( r2_hidden(E,J)
                                                    | r2_hidden(C,J)
                                                    | r2_hidden(G,J)
                                                    | r2_hidden(I,J)
                                                    | r2_hidden(B,K)
                                                    | r2_hidden(D,K)
                                                    | r2_hidden(F,K)
                                                    | r2_hidden(H,K)
                                                    | r2_analoaf(A,D,E,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(conmetr1,d3_conmetr1),
    []).

fof(d6_conmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v6_conmetr(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A)))
                                           => ! [K] : 
                                                ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A)))
                                               => ( ( v4_analmetr(J,A)
                                                    & v4_analmetr(K,A)
                                                    & r2_hidden(B,J)
                                                    & r2_hidden(D,J)
                                                    & r2_hidden(F,J)
                                                    & r2_hidden(H,J)
                                                    & r2_hidden(C,K)
                                                    & r2_hidden(E,K)
                                                    & r2_hidden(G,K)
                                                    & r2_hidden(I,K)
                                                    & r4_analmetr(A,D,C,H,G)
                                                    & r4_analmetr(A,C,B,G,F)
                                                    & r4_analmetr(A,B,E,F,I) )
                                                 => ( r2_hidden(E,J)
                                                    | r2_hidden(C,J)
                                                    | r2_hidden(G,J)
                                                    | r2_hidden(I,J)
                                                    | r2_hidden(B,K)
                                                    | r2_hidden(D,K)
                                                    | r2_hidden(F,K)
                                                    | r2_hidden(H,K)
                                                    | r4_analmetr(A,D,E,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(conmetr,d6_conmetr),
    []).

fof(dt_g1_analoaf,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
     => ( v1_analoaf(g1_analoaf(A,B))
        & l1_analoaf(g1_analoaf(A,B)) ) ) ),
    file(analoaf,g1_analoaf),
    []).

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

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

fof(dt_k3_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ( v1_analoaf(k3_analmetr(A))
        & l1_analoaf(k3_analmetr(A)) ) ) ),
    file(analmetr,k3_analmetr),
    []).

fof(dt_l1_analmetr,axiom,(
    ! [A] : 
      ( l1_analmetr(A)
     => l1_analoaf(A) ) ),
    file(analmetr,l1_analmetr),
    []).

fof(dt_l1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => l1_struct_0(A) ) ),
    file(analoaf,l1_analoaf),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_m1_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_u1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => m2_relset_1(u1_analoaf(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ),
    file(analoaf,u1_analoaf),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_analmetr,axiom,(
    ? [A] : l1_analmetr(A) ),
    file(analmetr,l1_analmetr),
    []).

fof(existence_l1_analoaf,axiom,(
    ? [A] : l1_analoaf(A) ),
    file(analoaf,l1_analoaf),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_m1_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_1),
    []).

fof(fc2_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A)) ) ) ),
    file(analmetr,fc2_analmetr),
    []).

fof(fc3_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A)) ) ) ),
    file(analmetr,fc3_analmetr),
    []).

fof(fc4_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v2_diraf(k3_analmetr(A)) ) ) ),
    file(analmetr,fc4_analmetr),
    []).

fof(free_g1_analoaf,axiom,(
    ! [A,B] : 
      ( m1_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
     => ! [C,D] : 
          ( g1_analoaf(A,B) = g1_analoaf(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(analoaf,g1_analoaf),
    []).

fof(rc2_analmetr,axiom,(
    ? [A] : 
      ( l1_analmetr(A)
      & ~ v3_struct_0(A) ) ),
    file(analmetr,rc2_analmetr),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

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

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

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

fof(t47_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
        <=> m1_subset_1(B,u1_struct_0(k3_analmetr(A))) ) ) ),
    file(analmetr,t47_analmetr),
    []).

fof(t48_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k3_analmetr(A)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k3_analmetr(A)))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(k3_analmetr(A)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u1_struct_0(k3_analmetr(A)))
                                     => ( ( B = F
                                          & C = G
                                          & D = H
                                          & E = I )
                                       => ( r4_analmetr(A,B,C,D,E)
                                        <=> r2_analoaf(k3_analmetr(A),F,G,H,I) ) ) ) ) ) ) ) ) ) ) ) ),
    file(analmetr,t48_analmetr),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t57_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analmetr(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
        <=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_analmetr(A)))) ) ) ),
    file(analmetr,t57_analmetr),
    []).

fof(t58_analmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_analmetr(A))))
             => ( B = C
               => ( v4_analmetr(B,A)
                <=> v1_aff_1(C,k3_analmetr(A)) ) ) ) ) ) ),
    file(analmetr,t58_analmetr),
    []).