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<div class="add">

<a NAME="E1:30_1_1"/>
not  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="pboole.html#K10" title="PBOOLE:func.10">MSFuncs</a> <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c2">D</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#T149" title="PBOOLE:th.149">PBOOLE:149</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">X</font> =  <a href="card_3.html#K4" title="CARD_3:func.4">product</a> <span class="p1">(<span class="default"><a href="pboole.html#K10" title="PBOOLE:func.10">MSFuncs</a> <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c2">D</font></span>)</span> as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  <b>by </b><i><a class="ref" href="card_3.html#T37" title="CARD_3:th.37">CARD_3:37</a></i>;<br/>
<a NAME="E3:30_1_1"/>
<font color="Maroon" title="c3">X</font> is    <a href="autalg_1.html#M1" title="AUTALG_1:mode.1">MSFunctionSet</a> of <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c2">D</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:30_1_1_1"/>
<font color="Maroon" title="c2">D</font> <a href="pzfmisc1.html#R1" title="PZFMISC1:pred.1">is_transformable_to</a> <font color="Maroon" title="c2">D</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="autalg_1.html#D6" target="_self" title="AUTALG_1:def.6">AUTALG_1:def 6</a><br/>

<b>let </b><font color="Maroon" title="c4">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E2:30_1_1_1"/>
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 ;<br/>

<b>hence </b><a NAME="E3:30_1_1_1"/>
<font color="Maroon" title="c4">x</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c2">D</font>
 <b>by </b><i><a class="ref" href="autalg_1.html#T21" target="_self" title="AUTALG_1:th.21">Th21</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c4">X</font> = <font color="Maroon" title="c3">X</font> as    <a href="autalg_1.html#M1" title="AUTALG_1:mode.1">MSFunctionSet</a> of <font color="Maroon" title="c2">D</font>,<font color="Maroon" title="c2">D</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c4">X</font>
;<br/>

<b>thus </b><a NAME="E5:30_1_1"/>
not <font color="Maroon" title="c4">X</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ;<br/>


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