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<a NAME="E1:27_1_1"/>
 <a href="pboole.html#K11" title="PBOOLE:func.11">MSFuncs</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font> is <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>
 
<b>by </b><i><a class="txt" href="autalg_1.html#E1:27"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="autalg_1.html#T23" target="_self" title="AUTALG_1:th.23">Th23</a></i>;<br/>
<a NAME="E2:27_1_1"/><b>then </b>
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#K11" title="PBOOLE:func.11">MSFuncs</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</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="c4">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#K11" title="PBOOLE:func.11">MSFuncs</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</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/>
<b>take </b>
<font color="Maroon" title="c4">X</font>
;<br/>

<b>let </b><font color="Maroon" title="c5">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E4:27_1_1"/>
<font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">X</font>
 ;<br/>

<b>hence </b><a NAME="E5:27_1_1"/>
<font color="Maroon" title="c5">x</font> is    <a href="pboole.html#M3" title="PBOOLE:mode.3">ManySortedFunction</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c3">B</font>
 <b>by </b><i><a class="txt" href="autalg_1.html#E1:27"><i><font color="Green" title="E19">A1</font></i></a>, <a class="ref" href="autalg_1.html#T21" target="_self" title="AUTALG_1:th.21">Th21</a></i>;<br/>


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