fof(t3_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r2_analoaf(A,B,B,B,B) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_afvect0]),
    [file(afvect0,t3_afvect0),interesting(1.00)]).

fof(t2_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_analoaf(A,B,C,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_afvect0,d1_afvect0]),
    [file(afvect0,t2_afvect0),interesting(0.96)]).

fof(t7_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => r2_analoaf(A,B,B,C,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_afvect0,t4_afvect0,d1_afvect0]),
    [file(afvect0,t7_afvect0),interesting(0.96)]).

fof(l72_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => v6_rlvect_1(k5_afvect0(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_rlvect_1,t35_afvect0,t39_afvect0,d5_afvect0,d8_afvect0,d7_afvect0]),
    [file(afvect0,l72_afvect0),interesting(0.88)]).

fof(t21_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( r2_afvect0(A,B,C,D)
                   => r2_afvect0(A,D,C,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_afvect0,t8_afvect0,t4_afvect0,d3_afvect0]),
    [file(afvect0,t21_afvect0),interesting(0.87)]).

fof(t23_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_afvect0(A,B,C,B)
              <=> ( B = C
                  | r1_afvect0(A,B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_afvect0,d2_afvect0,t7_afvect0,d3_afvect0,d2_afvect0,d3_afvect0]),
    [file(afvect0,t23_afvect0),interesting(0.84)]).

fof(t16_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ? [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
          & ? [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
              & B != C
              & ~ r1_afvect0(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_realset2,d1_afvect0,t4_afvect0,d1_afvect0,t4_afvect0,t8_afvect0,d2_afvect0,d1_afvect0,t8_afvect0,t5_afvect0]),
    [file(afvect0,t16_afvect0),interesting(0.83)]).

fof(t22_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_afvect0(A,B,C,C)
              <=> B = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_afvect0,d1_afvect0,t7_afvect0,d3_afvect0]),
    [file(afvect0,t22_afvect0),interesting(0.82)]).

fof(t36_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_afvect0(A,B,k1_afvect0(A,B,C)) = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_afvect0,t21_afvect0,d4_afvect0]),
    [file(afvect0,t36_afvect0),interesting(0.81)]).

fof(t37_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( k1_afvect0(A,B,C) = k1_afvect0(A,B,D)
                   => C = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_afvect0]),
    [file(afvect0,t37_afvect0),interesting(0.80)]).

fof(t45_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( k1_afvect0(A,B,k1_afvect0(A,C,D)) = k1_afvect0(A,C,k1_afvect0(A,B,D))
                  <=> ~ ( B != C
                        & ~ r1_afvect0(A,B,C)
                        & ~ r1_afvect0(A,C,k1_afvect0(A,B,C)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_afvect0,t44_afvect0,t43_afvect0,d4_afvect0,t23_afvect0,t23_afvect0,t23_afvect0,d4_afvect0,t43_afvect0,t44_afvect0,t36_afvect0]),
    [file(afvect0,t45_afvect0),interesting(0.80)]).

fof(t41_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( r1_afvect0(A,B,C)
                  <=> r1_afvect0(A,k1_afvect0(A,D,B),k1_afvect0(A,D,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_afvect0,t37_afvect0,t40_afvect0,d2_afvect0,d2_afvect0,t40_afvect0,d2_afvect0]),
    [file(afvect0,t41_afvect0),interesting(0.79)]).

fof(t5_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( r2_analoaf(A,B,C,B,D)
                   => C = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_afvect0,t4_afvect0,d1_afvect0]),
    [file(afvect0,t5_afvect0),interesting(0.78)]).

fof(t35_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_afvect0(A,B,C) = C
              <=> ( C = B
                  | r1_afvect0(A,C,B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_afvect0,t23_afvect0,t23_afvect0,d4_afvect0]),
    [file(afvect0,t35_afvect0),interesting(0.78)]).

fof(t71_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_analoaf(A)
        & v2_tdgroup(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => A = k2_tdgroup(k5_afvect0(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t9_tdgroup,t7_mcart_1,t10_mcart_1,t10_mcart_1,t23_mcart_1,t10_mcart_1,d4_tdgroup,d7_afvect0,d5_afvect0,t13_afvect0,d2_analoaf,t7_mcart_1,t10_mcart_1,t10_mcart_1,t23_mcart_1,t10_mcart_1,d2_analoaf,d7_afvect0,d5_afvect0,t8_afvect0,t13_afvect0,d5_afvect0,d4_tdgroup,d2_relat_1,t9_tdgroup]),
    [file(afvect0,t71_afvect0),interesting(0.78)]).

fof(t4_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( r2_analoaf(A,B,C,D,E)
                       => r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_afvect0,d1_afvect0]),
    [file(afvect0,t4_afvect0),interesting(0.77)]).

fof(t8_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( r2_analoaf(A,B,C,D,E)
                       => r2_analoaf(A,C,B,E,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_afvect0,d1_afvect0]),
    [file(afvect0,t8_afvect0),interesting(0.77)]).

fof(t39_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => r2_analoaf(A,B,C,k1_afvect0(A,D,C),k1_afvect0(A,D,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_afvect0,t30_afvect0]),
    [file(afvect0,t39_afvect0),interesting(0.77)]).

fof(t28_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( ( r2_afvect0(A,B,C,D)
                          & r1_afvect0(A,C,E) )
                       => r2_afvect0(A,B,E,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_afvect0,d3_afvect0,d1_afvect0,t4_afvect0,d1_afvect0,t8_afvect0,d1_afvect0,d1_afvect0,d1_afvect0,d3_afvect0]),
    [file(afvect0,t28_afvect0),interesting(0.77)]).

fof(t38_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                  & k1_afvect0(A,B,D) = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_afvect0]),
    [file(afvect0,t38_afvect0),interesting(0.77)]).

fof(t24_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                  & r2_afvect0(A,B,D,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_afvect0,d3_afvect0]),
    [file(afvect0,t24_afvect0),interesting(0.77)]).

fof(t26_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                  & r2_afvect0(A,B,C,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_afvect0,d3_afvect0]),
    [file(afvect0,t26_afvect0),interesting(0.77)]).

fof(t43_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( k1_afvect0(A,B,C) = k1_afvect0(A,D,C)
                  <=> ( B = D
                      | r1_afvect0(A,B,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_afvect0,t25_afvect0,d4_afvect0,t29_afvect0]),
    [file(afvect0,t43_afvect0),interesting(0.76)]).

fof(t25_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ~ ( r2_afvect0(A,B,C,D)
                          & r2_afvect0(A,B,E,D)
                          & C != E
                          & ~ r1_afvect0(A,C,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_afvect0,d1_afvect0,t4_afvect0,d1_afvect0,d1_afvect0,d1_afvect0,t8_afvect0,d1_afvect0,d2_afvect0]),
    [file(afvect0,t25_afvect0),interesting(0.72)]).

fof(l70_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
             => k2_rlvect_1(k5_afvect0(A,B),C,k1_rlvect_1(k5_afvect0(A,B))) = C ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_afvect0,d5_afvect0,t5_afvect0]),
    [file(afvect0,l70_afvect0),interesting(0.70)]).

fof(t18_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ~ ( r1_afvect0(A,B,C)
                      & r1_afvect0(A,B,D)
                      & C != D
                      & ~ r1_afvect0(A,C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_afvect0,t4_afvect0,d2_afvect0,d1_afvect0,d1_afvect0,d1_afvect0,d1_afvect0,d2_afvect0]),
    [file(afvect0,t18_afvect0),interesting(0.69)]).

fof(l68_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k5_afvect0(A,B)))
                 => k2_rlvect_1(k5_afvect0(A,B),C,D) = k2_rlvect_1(k5_afvect0(A,B),D,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_afvect0,d5_afvect0,d1_afvect0,d5_afvect0,d7_afvect0]),
    [file(afvect0,l68_afvect0),interesting(0.68)]).

fof(t29_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                         => ( ( r2_afvect0(A,B,C,D)
                              & r2_afvect0(A,B,E,F)
                              & r1_afvect0(A,C,E) )
                           => D = F ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t28_afvect0,t27_afvect0]),
    [file(afvect0,t29_afvect0),interesting(0.68)]).

fof(l71_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v3_rlvect_1(k5_afvect0(A,B))
            & v4_rlvect_1(k5_afvect0(A,B))
            & v5_rlvect_1(k5_afvect0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l68_afvect0,d5_rlvect_1,l69_afvect0,d6_rlvect_1,l70_afvect0,d7_rlvect_1]),
    [file(afvect0,l71_afvect0),interesting(0.64)]).

fof(t66_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
             => ? [D] : 
                  ( m1_subset_1(D,u1_struct_0(k5_afvect0(A,B)))
                  & k4_rlvect_1(k5_afvect0(A,B),D,D) = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_afvect0,d5_afvect0,d7_afvect0]),
    [file(afvect0,t66_afvect0),interesting(0.60)]).

fof(t67_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_tdgroup(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
             => ( k4_rlvect_1(k5_afvect0(A,B),C,C) = k1_rlvect_1(k5_afvect0(A,B))
               => C = k1_rlvect_1(k5_afvect0(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_afvect0,d5_afvect0,t2_afvect0,t21_tdgroup]),
    [file(afvect0,t67_afvect0),interesting(0.58)]).

fof(l69_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k5_afvect0(A,B)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k5_afvect0(A,B)))
                     => k2_rlvect_1(k5_afvect0(A,B),k2_rlvect_1(k5_afvect0(A,B),C,D),E) = k2_rlvect_1(k5_afvect0(A,B),C,k2_rlvect_1(k5_afvect0(A,B),D,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_afvect0,d5_afvect0,d7_afvect0,d5_afvect0,d1_afvect0,t4_afvect0,t4_afvect0,d1_afvect0,d1_afvect0,t4_afvect0,d7_afvect0,d5_afvect0,t8_afvect0,d1_afvect0,d1_afvect0,d1_afvect0,d1_afvect0,t8_afvect0,t4_afvect0,d7_afvect0,d5_afvect0,t4_afvect0,d1_afvect0,t5_afvect0]),
    [file(afvect0,l69_afvect0),interesting(0.57)]).

fof(l54_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( k1_afvect0(A,B,C) = D
                  <=> r2_analoaf(A,C,B,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_afvect0,d3_afvect0,d3_afvect0,d4_afvect0]),
    [file(afvect0,l54_afvect0),interesting(0.56)]).

fof(t33_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( k1_afvect0(A,B,C) = D
                  <=> r2_analoaf(A,C,B,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_afvect0,d3_afvect0,d3_afvect0,d4_afvect0]),
    [file(afvect0,t33_afvect0),interesting(0.55)]).

fof(t58_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( C = D
                   => k5_rlvect_1(k5_afvect0(A,B),C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),k4_afvect0(A,B),D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t35_afvect0,t39_afvect0,d5_afvect0,d8_afvect0,d7_afvect0,d10_rlvect_1]),
    [file(afvect0,t58_afvect0),interesting(0.55)]).

fof(t31_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                             => ( ( r2_afvect0(A,B,C,D)
                                  & r2_afvect0(A,E,F,G)
                                  & r1_afvect0(A,C,F) )
                               => r2_analoaf(A,B,E,G,D) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t28_afvect0,t30_afvect0]),
    [file(afvect0,t31_afvect0),interesting(0.52)]).

fof(t72_afvect0,theorem,(
    ! [A] : 
      ( ( v1_analoaf(A)
        & l1_analoaf(A) )
     => ( ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_tdgroup(A)
          & l1_analoaf(A) )
      <=> ? [B] : 
            ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v13_vectsp_1(B)
            & ~ v3_realset2(B)
            & v1_tdgroup(B)
            & l1_rlvect_1(B)
            & A = k2_tdgroup(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t71_afvect0]),
    [file(afvect0,t72_afvect0),interesting(0.28)]).

fof(t70_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & ~ v3_realset2(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ( ~ v3_struct_0(k2_tdgroup(A))
        & ~ v3_realset2(k2_tdgroup(A))
        & v2_tdgroup(k2_tdgroup(A))
        & l1_analoaf(k2_tdgroup(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_realset2,t22_tdgroup]),
    [file(afvect0,t70_afvect0),interesting(0.27)]).

fof(t78_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & ~ v3_realset2(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A)))
             => ( C = B
               => r4_afvect0(A,k5_afvect0(k2_tdgroup(A),C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s4_funct_2,t9_tdgroup,t76_afvect0,t77_afvect0,t75_afvect0,t75_afvect0,t75_afvect0,t58_afvect0,d10_afvect0,d11_afvect0]),
    [file(afvect0,t78_afvect0),interesting(0.24)]).

fof(d7_afvect0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
                & m2_relset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) )
             => ( C = k3_afvect0(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,D,E) = k2_afvect0(A,B,D,E) ) ) ) ) ) ) ),
    file(afvect0,d7_afvect0),
    [interesting(0.00)]).

fof(d5_afvect0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( E = k2_afvect0(A,B,C,D)
                      <=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ),
    file(afvect0,d5_afvect0),
    [interesting(0.00)]).

fof(d1_afvect0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v1_afvect0(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))
                     => ( r2_analoaf(A,B,C,D,D)
                       => B = C ) ) ) )
          & ! [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))
                                 => ( ( r2_analoaf(A,B,C,F,G)
                                      & r2_analoaf(A,D,E,F,G) )
                                   => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) )
          & ! [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))
                          & r2_analoaf(A,B,C,D,E) ) ) ) )
          & ! [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))
                                 => ( ( r2_analoaf(A,B,C,E,F)
                                      & r2_analoaf(A,B,D,E,G) )
                                   => r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) )
          & ! [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))
                      & r2_analoaf(A,B,D,D,C) ) ) )
          & ! [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))
                         => ( r2_analoaf(A,B,C,D,E)
                           => r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ) ),
    file(afvect0,d1_afvect0),
    [interesting(0.00)]).

fof(d5_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v3_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B) ) ) ) ) ),
    file(rlvect_1,d5_rlvect_1),
    [interesting(0.00)]).

fof(d6_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v4_rlvect_1(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))
                   => k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D)) ) ) ) ) ) ),
    file(rlvect_1,d6_rlvect_1),
    [interesting(0.00)]).

fof(d7_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v5_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => k2_rlvect_1(A,B,k1_rlvect_1(A)) = B ) ) ) ),
    file(rlvect_1,d7_rlvect_1),
    [interesting(0.00)]).

fof(d8_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ( v6_rlvect_1(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) ),
    file(rlvect_1,d8_rlvect_1),
    [interesting(0.00)]).

fof(d4_afvect0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( D = k1_afvect0(A,B,C)
                  <=> r2_afvect0(A,C,B,D) ) ) ) ) ) ),
    file(afvect0,d4_afvect0),
    [interesting(0.00)]).

fof(d3_afvect0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => ( r2_afvect0(A,B,C,D)
                  <=> r2_analoaf(A,B,C,C,D) ) ) ) ) ) ),
    file(afvect0,d3_afvect0),
    [interesting(0.00)]).

fof(d2_afvect0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_afvect0(A,B,C)
              <=> ( r2_analoaf(A,B,C,C,B)
                  & B != C ) ) ) ) ) ),
    file(afvect0,d2_afvect0),
    [interesting(0.00)]).

fof(t30_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                         => ( ( r2_afvect0(A,B,C,D)
                              & r2_afvect0(A,E,C,F) )
                           => r2_analoaf(A,B,E,F,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_afvect0,t4_afvect0,d3_afvect0,t8_afvect0,d1_afvect0,d3_afvect0,t8_afvect0,d1_afvect0,d1_afvect0,d1_afvect0]),
    [file(afvect0,t30_afvect0),interesting(0.00)]).

fof(d8_afvect0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( C = k4_afvect0(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) = k1_afvect0(A,B,D) ) ) ) ) ) ),
    file(afvect0,d8_afvect0),
    [interesting(0.00)]).

fof(t10_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                                 => ( ( r2_analoaf(A,B,C,D,E)
                                      & r2_analoaf(A,F,G,B,C)
                                      & r2_analoaf(A,F,H,D,E) )
                                   => G = H ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t4_afvect0,d1_afvect0,d1_afvect0,t5_afvect0]),
    [file(afvect0,t10_afvect0),interesting(0.00)]).

fof(t11_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                                 => ( ( r2_analoaf(A,B,C,D,E)
                                      & r2_analoaf(A,F,G,C,B)
                                      & r2_analoaf(A,F,H,E,D) )
                                   => G = H ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t4_afvect0,t8_afvect0,d1_afvect0,d1_afvect0,t5_afvect0]),
    [file(afvect0,t11_afvect0),interesting(0.00)]).

fof(t12_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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,u1_struct_0(A))
                                         => ! [K] : 
                                              ( m1_subset_1(K,u1_struct_0(A))
                                             => ( ( r2_analoaf(A,B,C,D,E)
                                                  & r2_analoaf(A,F,G,H,I)
                                                  & r2_analoaf(A,C,J,F,G)
                                                  & r2_analoaf(A,E,K,H,I) )
                                               => r2_analoaf(A,B,J,D,K) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_afvect0,d1_afvect0,t8_afvect0,d1_afvect0]),
    [file(afvect0,t12_afvect0),interesting(0.00)]).

fof(t14_afvect0,theorem,(
    $true ),
    file(afvect0,t14_afvect0),
    [interesting(0.00)]).

fof(t15_afvect0,theorem,(
    $true ),
    file(afvect0,t15_afvect0),
    [interesting(0.00)]).

fof(d7_realset2,definition,(
    ! [A] : 
      ( l1_struct_0(A)
     => ( v3_realset2(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => B = C ) ) ) ) ),
    file(realset2,d7_realset2),
    [interesting(0.00)]).

fof(t17_afvect0,theorem,(
    $true ),
    file(afvect0,t17_afvect0),
    [interesting(0.00)]).

fof(t19_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( ( r1_afvect0(A,B,C)
                          & r2_analoaf(A,B,C,D,E) )
                       => r1_afvect0(A,D,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_afvect0,t4_afvect0,t8_afvect0,d1_afvect0,d1_afvect0,d2_afvect0,d1_afvect0]),
    [file(afvect0,t19_afvect0),interesting(0.00)]).

fof(t1_afvect0,theorem,(
    $true ),
    file(afvect0,t1_afvect0),
    [interesting(0.00)]).

fof(t20_afvect0,theorem,(
    $true ),
    file(afvect0,t20_afvect0),
    [interesting(0.00)]).

fof(t32_afvect0,theorem,(
    $true ),
    file(afvect0,t32_afvect0),
    [interesting(0.00)]).

fof(t34_afvect0,theorem,(
    $true ),
    file(afvect0,t34_afvect0),
    [interesting(0.00)]).

fof(t40_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                         => ( r2_analoaf(A,B,C,D,E)
                          <=> r2_analoaf(A,k1_afvect0(A,F,B),k1_afvect0(A,F,C),k1_afvect0(A,F,D),k1_afvect0(A,F,E)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t39_afvect0,t4_afvect0,d1_afvect0,t4_afvect0,d1_afvect0,t8_afvect0,t39_afvect0,t39_afvect0,d1_afvect0,t8_afvect0,d1_afvect0]),
    [file(afvect0,t40_afvect0),interesting(0.00)]).

fof(t42_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( r2_afvect0(A,B,C,D)
                      <=> r2_afvect0(A,k1_afvect0(A,E,B),k1_afvect0(A,E,C),k1_afvect0(A,E,D)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_afvect0,t40_afvect0,d3_afvect0,d3_afvect0,t40_afvect0,d3_afvect0]),
    [file(afvect0,t42_afvect0),interesting(0.00)]).

fof(t44_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                 => k1_afvect0(A,B,k1_afvect0(A,C,k1_afvect0(A,B,D))) = k1_afvect0(A,k1_afvect0(A,B,C),D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_afvect0,t42_afvect0,d4_afvect0,t36_afvect0]),
    [file(afvect0,t44_afvect0),interesting(0.00)]).

fof(t27_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => ( ( r2_afvect0(A,B,C,D)
                          & r2_afvect0(A,B,C,E) )
                       => D = E ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_afvect0,t4_afvect0,d1_afvect0,t5_afvect0]),
    [file(afvect0,t27_afvect0),interesting(0.00)]).

fof(t46_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                     => k1_afvect0(A,B,k1_afvect0(A,C,k1_afvect0(A,D,E))) = k1_afvect0(A,D,k1_afvect0(A,C,k1_afvect0(A,B,E))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t39_afvect0,t36_afvect0,t39_afvect0,t36_afvect0,t4_afvect0,d1_afvect0,d3_afvect0,d4_afvect0,t35_afvect0,t39_afvect0,t39_afvect0,t4_afvect0,d1_afvect0,t39_afvect0,t4_afvect0,d1_afvect0,t39_afvect0,t39_afvect0,t4_afvect0,d1_afvect0,t39_afvect0,t4_afvect0,d1_afvect0,d1_afvect0,t8_afvect0,t5_afvect0]),
    [file(afvect0,t46_afvect0),interesting(0.00)]).

fof(t47_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                          & k1_afvect0(A,B,k1_afvect0(A,C,k1_afvect0(A,D,E))) = k1_afvect0(A,F,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_afvect0,d4_afvect0,t26_afvect0,d4_afvect0,t44_afvect0,t44_afvect0,t36_afvect0,t46_afvect0,t36_afvect0,t36_afvect0,t46_afvect0]),
    [file(afvect0,t47_afvect0),interesting(0.00)]).

fof(t48_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                      & k1_afvect0(A,B,k1_afvect0(A,E,C)) = k1_afvect0(A,E,k1_afvect0(A,D,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_afvect0,d4_afvect0,t44_afvect0,t36_afvect0]),
    [file(afvect0,t48_afvect0),interesting(0.00)]).

fof(t49_afvect0,theorem,(
    $true ),
    file(afvect0,t49_afvect0),
    [interesting(0.00)]).

fof(t50_afvect0,theorem,(
    $true ),
    file(afvect0,t50_afvect0),
    [interesting(0.00)]).

fof(t51_afvect0,theorem,(
    $true ),
    file(afvect0,t51_afvect0),
    [interesting(0.00)]).

fof(t52_afvect0,theorem,(
    $true ),
    file(afvect0,t52_afvect0),
    [interesting(0.00)]).

fof(t53_afvect0,theorem,(
    $true ),
    file(afvect0,t53_afvect0),
    [interesting(0.00)]).

fof(t54_afvect0,theorem,(
    $true ),
    file(afvect0,t54_afvect0),
    [interesting(0.00)]).

fof(t55_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( u1_struct_0(k5_afvect0(A,B)) = u1_struct_0(A)
            & u1_rlvect_1(k5_afvect0(A,B)) = k3_afvect0(A,B)
            & u2_struct_0(k5_afvect0(A,B)) = B ) ) ) ),
    file(afvect0,t55_afvect0),
    [interesting(0.00)]).

fof(t56_afvect0,theorem,(
    $true ),
    file(afvect0,t56_afvect0),
    [interesting(0.00)]).

fof(t57_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k5_afvect0(A,B)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( C = E
                              & D = F )
                           => k2_rlvect_1(k5_afvect0(A,B),C,D) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),k3_afvect0(A,B),E,F) ) ) ) ) ) ) ) ),
    file(afvect0,t57_afvect0),
    [interesting(0.00)]).

fof(t59_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_rlvect_1(k5_afvect0(A,B)) = B ) ) ),
    file(afvect0,t59_afvect0),
    [interesting(0.00)]).

fof(t60_afvect0,theorem,(
    $true ),
    file(afvect0,t60_afvect0),
    [interesting(0.00)]).

fof(t61_afvect0,theorem,(
    $true ),
    file(afvect0,t61_afvect0),
    [interesting(0.00)]).

fof(t62_afvect0,theorem,(
    $true ),
    file(afvect0,t62_afvect0),
    [interesting(0.00)]).

fof(t63_afvect0,theorem,(
    $true ),
    file(afvect0,t63_afvect0),
    [interesting(0.00)]).

fof(t64_afvect0,theorem,(
    $true ),
    file(afvect0,t64_afvect0),
    [interesting(0.00)]).

fof(t65_afvect0,theorem,(
    $true ),
    file(afvect0,t65_afvect0),
    [interesting(0.00)]).

fof(t21_tdgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( ( ~ ! [B] : 
                ( m1_subset_1(B,u1_struct_0(A))
               => ! [C] : 
                    ( m1_subset_1(C,u1_struct_0(A))
                   => B = C ) )
          & ! [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))
                     => ( r2_analoaf(A,B,C,D,D)
                       => B = C ) ) ) )
          & ! [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))
                                 => ( ( r2_analoaf(A,B,C,F,G)
                                      & r2_analoaf(A,D,E,F,G) )
                                   => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) )
          & ! [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))
                          & r2_analoaf(A,B,C,D,E) ) ) ) )
          & ! [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))
                                 => ( ( r2_analoaf(A,B,C,E,F)
                                      & r2_analoaf(A,B,D,E,G) )
                                   => r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) )
          & ! [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))
                      & r2_analoaf(A,B,D,D,C) ) ) )
          & ! [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))
                         => ( ( r2_analoaf(A,B,C,C,D)
                              & r2_analoaf(A,B,E,E,D) )
                           => C = E ) ) ) ) )
          & ! [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))
                         => ( r2_analoaf(A,B,C,D,E)
                           => r2_analoaf(A,B,D,C,E) ) ) ) ) ) )
      <=> ( ~ v3_struct_0(A)
          & ~ v3_realset2(A)
          & v2_tdgroup(A)
          & l1_analoaf(A) ) ) ) ),
    file(tdgroup,t21_tdgroup),
    [interesting(0.00)]).

fof(t68_afvect0,theorem,(
    $true ),
    file(afvect0,t68_afvect0),
    [interesting(0.00)]).

fof(t69_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_tdgroup(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ~ v3_struct_0(k5_afvect0(A,B))
            & v3_rlvect_1(k5_afvect0(A,B))
            & v4_rlvect_1(k5_afvect0(A,B))
            & v5_rlvect_1(k5_afvect0(A,B))
            & v6_rlvect_1(k5_afvect0(A,B))
            & v13_vectsp_1(k5_afvect0(A,B))
            & ~ v3_realset2(k5_afvect0(A,B))
            & v1_tdgroup(k5_afvect0(A,B))
            & l1_rlvect_1(k5_afvect0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_realset2,d7_realset2]),
    [file(afvect0,t69_afvect0),interesting(0.00)]).

fof(t6_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                         => ( ( r2_analoaf(A,B,C,D,E)
                              & r2_analoaf(A,B,C,D,F) )
                           => E = F ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t4_afvect0,d1_afvect0,t5_afvect0]),
    [file(afvect0,t6_afvect0),interesting(0.00)]).

fof(t22_tdgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ( ~ ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => B = C ) )
       => ( ~ v3_struct_0(k2_tdgroup(A))
          & ~ v3_realset2(k2_tdgroup(A))
          & v2_tdgroup(k2_tdgroup(A))
          & l1_analoaf(k2_tdgroup(A)) ) ) ) ),
    file(tdgroup,t22_tdgroup),
    [interesting(0.00)]).

fof(t9_tdgroup,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ( u1_struct_0(k2_tdgroup(A)) = u1_struct_0(A)
        & u1_analoaf(k2_tdgroup(A)) = k1_tdgroup(A) ) ) ),
    file(tdgroup,t9_tdgroup),
    [interesting(0.00)]).

fof(t7_mcart_1,theorem,(
    ! [A,B] : 
      ( k1_mcart_1(k4_tarski(A,B)) = A
      & k2_mcart_1(k4_tarski(A,B)) = B ) ),
    file(mcart_1,t7_mcart_1),
    [interesting(0.00)]).

fof(t10_mcart_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k2_zfmisc_1(B,C))
     => ( r2_hidden(k1_mcart_1(A),B)
        & r2_hidden(k2_mcart_1(A),C) ) ) ),
    file(mcart_1,t10_mcart_1),
    [interesting(0.00)]).

fof(t23_mcart_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(A,k2_zfmisc_1(B,C))
     => A = k4_tarski(k1_mcart_1(A),k2_mcart_1(A)) ) ),
    file(mcart_1,t23_mcart_1),
    [interesting(0.00)]).

fof(d4_tdgroup,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
         => ( B = k1_tdgroup(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))
                           => ( r2_hidden(k4_tarski(k4_tarski(C,D),k4_tarski(E,F)),B)
                            <=> k2_rlvect_1(A,C,F) = k2_rlvect_1(A,D,E) ) ) ) ) ) ) ) ) ),
    file(tdgroup,d4_tdgroup),
    [interesting(0.00)]).

fof(t13_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                             => ( ( r2_analoaf(A,B,C,D,E)
                                  & r2_analoaf(A,B,F,G,E) )
                               => r2_analoaf(A,C,F,G,D) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_afvect0,d1_afvect0,t4_afvect0,d1_afvect0,d1_afvect0,d1_afvect0]),
    [file(afvect0,t13_afvect0),interesting(0.00)]).

fof(d2_analoaf,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(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))
                     => ( r2_analoaf(A,B,C,D,E)
                      <=> r2_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),u1_analoaf(A)) ) ) ) ) ) ) ),
    file(analoaf,d2_analoaf),
    [interesting(0.00)]).

fof(d2_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( A = B
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
              <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d2_relat_1),
    [interesting(0.00)]).

fof(t73_afvect0,theorem,(
    $true ),
    file(afvect0,t73_afvect0),
    [interesting(0.00)]).

fof(t74_afvect0,theorem,(
    $true ),
    file(afvect0,t74_afvect0),
    [interesting(0.00)]).

fof(s4_funct_2,theorem,(
    ? [A] : 
      ( v1_funct_1(A)
      & v1_funct_2(A,f1_s4_funct_2,f2_s4_funct_2)
      & m2_relset_1(A,f1_s4_funct_2,f2_s4_funct_2)
      & ! [B] : 
          ( m1_subset_1(B,f1_s4_funct_2)
         => k8_funct_2(f1_s4_funct_2,f2_s4_funct_2,A,B) = f3_s4_funct_2(B) ) ) ),
    file(funct_2,s4_funct_2),
    [interesting(0.00)]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.00)]).

fof(t21_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(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))
                     => ( ( k2_rlvect_1(A,B,D) = k2_rlvect_1(A,B,E)
                          | k2_rlvect_1(A,D,B) = k2_rlvect_1(A,E,B) )
                       => D = E ) ) ) ) ) ) ),
    file(rlvect_1,t21_rlvect_1),
    [interesting(0.00)]).

fof(d8_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    [interesting(0.00)]).

fof(t76_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & ~ v3_realset2(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D) = k4_rlvect_1(A,C,D) )
               => v2_funct_1(B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t21_rlvect_1,d8_funct_1]),
    [file(afvect0,t76_afvect0),interesting(0.00)]).

fof(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    [interesting(0.00)]).

fof(t16_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A)
            & k2_rlvect_1(A,k5_rlvect_1(A,B),B) = k1_rlvect_1(A) ) ) ) ),
    file(rlvect_1,t16_rlvect_1),
    [interesting(0.00)]).

fof(t10_rlvect_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
            & k2_rlvect_1(A,k1_rlvect_1(A),B) = B ) ) ) ),
    file(rlvect_1,t10_rlvect_1),
    [interesting(0.00)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.00)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

fof(t77_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & ~ v3_realset2(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
                 => ( ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E) = k4_rlvect_1(A,C,E) )
                   => k2_relat_1(B) = u1_struct_0(k5_afvect0(k2_tdgroup(A),D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t12_relset_1,t9_tdgroup,d6_rlvect_1,t16_rlvect_1,t10_rlvect_1,d5_funct_1,d3_tarski,d10_xboole_0]),
    [file(afvect0,t77_afvect0),interesting(0.00)]).

fof(d5_tdgroup,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => k2_tdgroup(A) = g1_analoaf(u1_struct_0(A),k1_tdgroup(A)) ) ),
    file(tdgroup,d5_tdgroup),
    [interesting(0.00)]).

fof(t75_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v13_vectsp_1(A)
        & ~ v3_realset2(A)
        & v1_tdgroup(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A)))
                 => ( ( ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E) = k4_rlvect_1(A,C,E) )
                      & D = C )
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k4_rlvect_1(A,E,F)) = k1_binop_1(k3_afvect0(k2_tdgroup(A),D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,F))
                              & k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k1_rlvect_1(A)) = k1_rlvect_1(k5_afvect0(k2_tdgroup(A),D))
                              & k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,k5_rlvect_1(A,E)) = k1_funct_1(k4_afvect0(k2_tdgroup(A),D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_tdgroup,d7_afvect0,d5_afvect0,d2_analoaf,d4_tdgroup,d6_rlvect_1,d6_rlvect_1,t21_rlvect_1,t10_rlvect_1,d8_afvect0,l54_afvect0,d2_analoaf,d4_tdgroup,d6_rlvect_1,t21_rlvect_1,d6_rlvect_1,t16_rlvect_1,t10_rlvect_1]),
    [file(afvect0,t75_afvect0),interesting(0.00)]).

fof(d10_rlvect_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( v4_rlvect_1(A)
              & v5_rlvect_1(A)
              & v6_rlvect_1(A) )
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C = k5_rlvect_1(A,B)
                <=> k2_rlvect_1(A,B,C) = k1_rlvect_1(A) ) ) ) ) ) ),
    file(rlvect_1,d10_rlvect_1),
    [interesting(0.00)]).

fof(d10_afvect0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( r3_afvect0(A,B,C)
              <=> ( v2_funct_1(C)
                  & k2_relat_1(C) = u1_struct_0(B)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k2_rlvect_1(A,D,E)) = k2_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,E))
                            & k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k1_rlvect_1(A)) = k1_rlvect_1(B)
                            & k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,k5_rlvect_1(A,D)) = k5_rlvect_1(B,k8_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) ) ) ) ) ) ) ) ) ),
    file(afvect0,d10_afvect0),
    [interesting(0.00)]).

fof(d11_afvect0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_rlvect_1(B) )
         => ( r4_afvect0(A,B)
          <=> ? [C] : 
                ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
                & r3_afvect0(A,B,C) ) ) ) ) ),
    file(afvect0,d11_afvect0),
    [interesting(0.00)]).

fof(t9_afvect0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_afvect0(A)
        & l1_analoaf(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))
                         => ( ( r2_analoaf(A,B,C,D,E)
                              & r2_analoaf(A,B,D,F,E) )
                           => C = F ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_afvect0,t4_afvect0,t8_afvect0,t4_afvect0,t8_afvect0,d1_afvect0,t5_afvect0]),
    [file(afvect0,t9_afvect0),interesting(0.00)]).