% Mizar problem: t64_int_1,int_1,1139,27 
fof(t64_int_1,conjecture,(
    ! [A] : 
      ( v1_xreal_0(A)
     => k2_int_1(k2_int_1(A)) = k2_int_1(A) ) ),
    inference(mizar_bg_added,[status(thm)],[rc1_xreal_0,rc1_xcmplx_0,dt_k2_int_1,rc2_int_1,cc4_int_1,cc2_xreal_0,t54_int_1]),
    [file(int_1,t64_int_1)]).

fof(rc1_xreal_0,axiom,(
    ? [A] : 
      ( v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(xreal_0,rc1_xreal_0),
    []).

fof(rc1_xcmplx_0,axiom,(
    ? [A] : v1_xcmplx_0(A) ),
    file(xcmplx_0,rc1_xcmplx_0),
    []).

fof(dt_k2_int_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_int_1(k2_int_1(A)) ) ),
    file(int_1,k2_int_1),
    []).

fof(rc2_int_1,axiom,(
    ? [A] : v1_int_1(A) ),
    file(int_1,rc2_int_1),
    []).

fof(cc4_int_1,axiom,(
    ! [A] : 
      ( v1_int_1(A)
     => ( v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(int_1,cc4_int_1),
    []).

fof(cc2_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xcmplx_0(A) ) ),
    file(xreal_0,cc2_xreal_0),
    []).

fof(t54_int_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( k2_int_1(A) = A
      <=> v1_int_1(A) ) ) ),
    file(int_1,t54_int_1),
    []).