deletions | additions       diff --git a/untitled.tex b/untitled.tex  index 760ed79..0020975 100644  --- a/untitled.tex  +++ b/untitled.tex 
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(uu_x + uu_{xx} +v_xv_x + vv_{xx})(u^{2}+v^{2})  &-(uu_x + vv_x)(2uu_x+2vv_x)+(uu_y + uu_{yy} +v_yv_y + vv_{yy})(u^{2}+v^{2})-(uu_y + vv_y)(2uu_y+2vv_y)\\  &=u^{2}u^{2}_x+u^{3}u_{xx}+u^{2}v^{2}_x+u^{2}vv_{xx}+v^{2}u^{2}_x+v^{2}uu_{xx}+v^{2}v^{2}_x+v^{3}v_{xx}\\  &-2u^{2}u^{2}_x-2uvv_xu_x-2uvu_xv_x-2v^{2}v^{2}_x &-2u^{2}u^{2}_x-2uvv_xu_x-2uvu_xv_x-2v^{2}v^{2}_x+u^{2}u^{2}_y+u^{3}u_{yy}+u^{2}v^{2}_y+u^{2}vv_{yy}+\\  &v^{2}u^{2}_y+v^{2}uu_{yy}+v^{2}v^{2}_y+v^{3}v_{yy}-2u^{2}u^{2}_y-2uvv_yu_y-2uvu_yv_y-2v^{2}v^{2}_y  &-2u^{2}u^{2}_y-2uvv_yu_y-2uvu_yv_y-2v^{2}v^{2}_y  \end{align*}  \end{proof}