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<b>let </b><font color="Maroon">Y</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="realset2.html#V3">trivial</a>  <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">y</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">Y</font>;<br/>



<b>assume </b><a NAME="E1:19"/>
not <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">y</font></span><a href="domain_1.html#K6">}</a></span> is <a href="tex_2.html#V1" target="_self">proper</a>
 ;<br/>

<a NAME="E2:19"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">Y</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">y</font></span><a href="domain_1.html#K6">}</a></span>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E3:19"/>
contradiction
 <b>by </b><i><a class="ref" href="tex_1.html#D1">TEX_1:def 1</a></i>;<br/>


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