% Mizar problem: t1_jordan18,jordan18,48,47 
fof(t1_jordan18,conjecture,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => k5_square_1(k6_xcmplx_0(A,B)) = k5_square_1(k6_xcmplx_0(B,A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc2_xreal_0,dt_k4_xcmplx_0,dt_k5_square_1,dt_k6_xcmplx_0,fc1_square_1,fc1_xreal_0,fc2_square_1,fc5_xreal_0,involutiveness_k4_xcmplx_0,rc1_xreal_0,t61_square_1]),
    [file(jordan18,t1_jordan18)]).

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

fof(dt_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k4_xcmplx_0(A)) ) ),
    file(xcmplx_0,k4_xcmplx_0),
    []).

fof(dt_k5_square_1,axiom,(
    $true ),
    file(square_1,k5_square_1),
    []).

fof(dt_k6_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k6_xcmplx_0),
    []).

fof(fc1_square_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k5_square_1(A)) ) ),
    file(square_1,fc1_square_1),
    []).

fof(fc1_xreal_0,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_xcmplx_0(k4_xcmplx_0(A))
        & v1_xreal_0(k4_xcmplx_0(A)) ) ) ),
    file(xreal_0,fc1_xreal_0),
    []).

fof(fc2_square_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ( v1_xcmplx_0(k5_square_1(A))
        & v1_xreal_0(k5_square_1(A)) ) ) ),
    file(square_1,fc2_square_1),
    []).

fof(fc5_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( v1_xcmplx_0(k6_xcmplx_0(A,B))
        & v1_xreal_0(k6_xcmplx_0(A,B)) ) ) ),
    file(xreal_0,fc5_xreal_0),
    []).

fof(involutiveness_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ),
    file(xcmplx_0,k4_xcmplx_0),
    []).

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

fof(t61_square_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k5_square_1(A) = k5_square_1(k4_xcmplx_0(A)) ) ),
    file(square_1,t61_square_1),
    []).