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<b>let </b><font color="Maroon" title="c1">I</font> be  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> ;<br/><b>let </b><font color="Maroon" title="c2">A</font> be    <a href="pboole.html#M1" title="PBOOLE:mode.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>;<br/><b>let </b><font color="Maroon" title="c3">i</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">I</font>;<br/><b>let </b><font color="Maroon" title="c4">S</font> be  non <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>







<b>take </b><font color="Maroon" title="c5">a</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="polynom1.html#K2" title="POLYNOM1:func.2">+*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">S</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">i</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_1.html#D16" target="_self" title="PENCIL_1:def.16">PENCIL_1:def 16</a><br/>

<a NAME="E1:36"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E2:36"/><b>then </b>
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">A</font>
 
;<br/>
<a NAME="E3:36"/><b>then </b>
<font color="Maroon" title="c3">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">A</font> <a href="polynom1.html#K2" title="POLYNOM1:func.2">+*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">S</font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_7.html#T32" title="FUNCT_7:th.32">FUNCT_7:32</a></i>;<br/>
<b>hence </b><a NAME="E4:36"/>
<font color="Maroon" title="c5">a</font> <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"><font color="Maroon" title="c2">A</font> <a href="polynom1.html#K2" title="POLYNOM1:func.2">+*</a> <font color="Maroon" title="c3">i</font>,<font color="Maroon" title="c4">S</font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>

<a NAME="E5:36"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">I</font>
 
<b>by </b><i><a class="ref" href="pboole.html#D3" title="PBOOLE:def.3">PBOOLE:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:36"/>
not <font color="Maroon" title="c5">a</font> is <a href="realset1.html#V1" title="REALSET1:attr.1">trivial</a>
 <b>by </b><i><a class="ref" href="funct_7.html#T33" title="FUNCT_7:th.33">FUNCT_7:33</a></i>;<br/>


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