% Mizar problem: t75_extreal2,extreal2,1807,52 
fof(t75_extreal2,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( ( A = k4_measure6
              | B = k4_measure6 )
           => k1_extreal2(A,B) = k4_measure6 ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k1_extreal2,connectedness_r1_supinf_1,d1_extreal2,dt_k1_extreal2,dt_k2_supinf_1,dt_k3_supinf_1,dt_k4_measure6,dt_k5_supinf_1,dt_m1_subset_1,existence_m1_subset_1,idempotence_k1_extreal2,redefinition_k4_measure6,redefinition_k5_supinf_1,reflexivity_r1_supinf_1,t21_supinf_1,t22_supinf_1]),
    [file(extreal2,t75_extreal2)]).

fof(commutativity_k1_extreal2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k1_extreal2(A,B) = k1_extreal2(B,A) ) ),
    file(extreal2,k1_extreal2),
    []).

fof(connectedness_r1_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => ( r1_supinf_1(A,B)
        | r1_supinf_1(B,A) ) ) ),
    file(supinf_1,r1_supinf_1),
    []).

fof(d1_extreal2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( ( r1_supinf_1(A,B)
             => k1_extreal2(A,B) = A )
            & ( ~ r1_supinf_1(A,B)
             => k1_extreal2(A,B) = B ) ) ) ) ),
    file(extreal2,d1_extreal2),
    []).

fof(dt_k1_extreal2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k1_extreal2(A,B),k3_supinf_1) ) ),
    file(extreal2,k1_extreal2),
    []).

fof(dt_k2_supinf_1,axiom,(
    $true ),
    file(supinf_1,k2_supinf_1),
    []).

fof(dt_k3_supinf_1,axiom,(
    $true ),
    file(supinf_1,k3_supinf_1),
    []).

fof(dt_k4_measure6,axiom,(
    m1_subset_1(k4_measure6,k3_supinf_1) ),
    file(measure6,k4_measure6),
    []).

fof(dt_k5_supinf_1,axiom,(
    m1_subset_1(k5_supinf_1,k3_supinf_1) ),
    file(supinf_1,k5_supinf_1),
    []).

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

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

fof(idempotence_k1_extreal2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k1_extreal2(A,A) = A ) ),
    file(extreal2,k1_extreal2),
    []).

fof(redefinition_k4_measure6,axiom,(
    k4_measure6 = k2_supinf_1 ),
    file(measure6,k4_measure6),
    []).

fof(redefinition_k5_supinf_1,axiom,(
    k5_supinf_1 = k2_supinf_1 ),
    file(supinf_1,k5_supinf_1),
    []).

fof(reflexivity_r1_supinf_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => r1_supinf_1(A,A) ) ),
    file(supinf_1,r1_supinf_1),
    []).

fof(t21_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => r1_supinf_1(k5_supinf_1,A) ) ),
    file(supinf_1,t21_supinf_1),
    []).

fof(t22_supinf_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => ( ( r1_supinf_1(A,B)
              & r1_supinf_1(B,A) )
           => A = B ) ) ) ),
    file(supinf_1,t22_supinf_1),
    []).