% Mizar problem: t15_euclmetr,euclmetr,461,64 
fof(t15_euclmetr,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( ( v1_euclmetr(A)
          & v3_euclmetr(A) )
       => v2_euclmetr(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_analmetr,dt_l1_analmetr,dt_l1_analoaf,dt_l1_struct_0,existence_l1_analmetr,existence_l1_analoaf,existence_l1_struct_0,rc2_analmetr,t10_euclmetr,t11_euclmetr,t13_conmetr,t15_conmetr,t8_euclmetr]),
    [file(euclmetr,t15_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(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(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(rc2_analmetr,axiom,(
    ? [A] : 
      ( l1_analmetr(A)
      & ~ v3_struct_0(A) ) ),
    file(analmetr,rc2_analmetr),
    []).

fof(t10_euclmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v2_euclmetr(A)
      <=> v2_conmetr(A) ) ) ),
    file(euclmetr,t10_euclmetr),
    []).

fof(t11_euclmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v3_euclmetr(A)
      <=> v1_conaffm(A) ) ) ),
    file(euclmetr,t11_euclmetr),
    []).

fof(t13_conmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( ( v1_conmetr(A)
          & v1_conaffm(A) )
       => v2_conmetr(A) ) ) ),
    file(conmetr,t13_conmetr),
    []).

fof(t15_conmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v3_conaffm(A)
       => v1_conmetr(A) ) ) ),
    file(conmetr,t15_conmetr),
    []).

fof(t8_euclmetr,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v1_euclmetr(A)
      <=> v3_conaffm(A) ) ) ),
    file(euclmetr,t8_euclmetr),
    []).