% Mizar problem: t9_euclmetr,euclmetr,203,48 
fof(t9_euclmetr,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v7_euclmetr(A)
      <=> v4_conaffm(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_analmetr,d4_conaffm,d7_euclmetr,dt_l1_analmetr,dt_l1_analoaf,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_analmetr,existence_l1_analoaf,existence_l1_struct_0,existence_m1_subset_1,rc2_analmetr]),
    [file(euclmetr,t9_euclmetr)]).

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(d4_conaffm,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v4_conaffm(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))
                                   => ( ( r5_analmetr(A,B,C,B,D)
                                        & r5_analmetr(A,B,E,B,F)
                                        & r5_analmetr(A,B,G,B,H)
                                        & r5_analmetr(A,C,E,D,F)
                                        & r5_analmetr(A,C,G,D,H) )
                                     => ( r4_analmetr(A,B,G,B,C)
                                        | r4_analmetr(A,B,C,B,E)
                                        | r5_analmetr(A,E,G,F,H) ) ) ) ) ) ) ) ) ) ) ) ),
    file(conaffm,d4_conaffm),
    []).

fof(d7_euclmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ( v7_euclmetr(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))
                                   => ( ( r5_analmetr(A,B,C,B,D)
                                        & r5_analmetr(A,B,E,B,F)
                                        & r5_analmetr(A,B,G,B,H)
                                        & r5_analmetr(A,C,E,D,F)
                                        & r5_analmetr(A,C,G,D,H) )
                                     => ( r4_analmetr(A,B,G,B,C)
                                        | r4_analmetr(A,B,C,B,E)
                                        | r5_analmetr(A,E,G,F,H) ) ) ) ) ) ) ) ) ) ) ) ),
    file(euclmetr,d7_euclmetr),
    []).

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_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

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_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

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