% Mizar problem: t12_conmetr1,conmetr1,1596,63 
fof(t12_conmetr1,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v6_conmetr1(A)
       => v5_conmetr1(A) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_l1_analoaf,dt_l1_struct_0,existence_l1_analoaf,existence_l1_struct_0,t10_conmetr1,t23_aff_2,t9_conmetr1]),
    [file(conmetr1,t12_conmetr1)]).

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_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(t10_conmetr1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v2_aff_2(A)
      <=> v6_conmetr1(A) ) ) ),
    file(conmetr1,t10_conmetr1),
    []).

fof(t23_aff_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v2_aff_2(A)
       => v13_aff_2(A) ) ) ),
    file(aff_2,t23_aff_2),
    []).

fof(t9_conmetr1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ( v13_aff_2(A)
      <=> v5_conmetr1(A) ) ) ),
    file(conmetr1,t9_conmetr1),
    []).