% Mizar problem: t5_extreal1,extreal1,56,14 
fof(t5_extreal1,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => k4_supinf_2(A,k3_supinf_2(B)) = k2_supinf_2(A,B) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_supinf_2,d4_supinf_2,dt_k2_supinf_2,dt_k3_supinf_1,dt_k3_supinf_2,dt_k4_supinf_2,dt_m1_subset_1,existence_m1_subset_1,involutiveness_k3_supinf_2]),
    [file(extreal1,t5_extreal1)]).

fof(commutativity_k2_supinf_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => k2_supinf_2(A,B) = k2_supinf_2(B,A) ) ),
    file(supinf_2,k2_supinf_2),
    []).

fof(d4_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => ! [B] : 
          ( m1_subset_1(B,k3_supinf_1)
         => k4_supinf_2(A,B) = k2_supinf_2(A,k3_supinf_2(B)) ) ) ),
    file(supinf_2,d4_supinf_2),
    []).

fof(dt_k2_supinf_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k2_supinf_2(A,B),k3_supinf_1) ) ),
    file(supinf_2,k2_supinf_2),
    []).

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

fof(dt_k3_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => m1_subset_1(k3_supinf_2(A),k3_supinf_1) ) ),
    file(supinf_2,k3_supinf_2),
    []).

fof(dt_k4_supinf_2,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k3_supinf_1)
        & m1_subset_1(B,k3_supinf_1) )
     => m1_subset_1(k4_supinf_2(A,B),k3_supinf_1) ) ),
    file(supinf_2,k4_supinf_2),
    []).

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(involutiveness_k3_supinf_2,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k3_supinf_1)
     => k3_supinf_2(k3_supinf_2(A)) = A ) ),
    file(supinf_2,k3_supinf_2),
    []).