% Mizar problem: t35_mcart_2,mcart_2,1007,52 
fof(t35_mcart_2,conjecture,(
    ! [A,B,C,D,E,F,G,H,I,J] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D)
        & r1_tarski(E,F)
        & r1_tarski(G,H)
        & r1_tarski(I,J) )
     => r1_tarski(k2_mcart_2(A,C,E,G,I),k2_mcart_2(B,D,F,H,J)) ) ),
    inference(mizar_bg_added,[status(thm)],[d2_mcart_2,dt_k1_zfmisc_1,dt_k2_mcart_2,dt_k2_zfmisc_1,dt_k4_zfmisc_1,dt_m1_subset_1,existence_m1_subset_1,reflexivity_r1_tarski,t119_zfmisc_1,t3_subset,t88_mcart_1]),
    [file(mcart_2,t35_mcart_2)]).

fof(d2_mcart_2,axiom,(
    ! [A,B,C,D,E] : k2_mcart_2(A,B,C,D,E) = k2_zfmisc_1(k4_zfmisc_1(A,B,C,D),E) ),
    file(mcart_2,d2_mcart_2),
    []).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_mcart_2,axiom,(
    $true ),
    file(mcart_2,k2_mcart_2),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

fof(dt_k4_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k4_zfmisc_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(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(t119_zfmisc_1,axiom,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) ),
    file(zfmisc_1,t119_zfmisc_1),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t88_mcart_1,axiom,(
    ! [A,B,C,D,E,F,G,H] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D)
        & r1_tarski(E,F)
        & r1_tarski(G,H) )
     => r1_tarski(k4_zfmisc_1(A,C,E,G),k4_zfmisc_1(B,D,F,H)) ) ),
    file(mcart_1,t88_mcart_1),
    []).