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<b>consider </b><font color="Maroon">O</font> being  <a href="struct_0.html#V1">strict</a> 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>reconsider </b><font color="Maroon">tau</font> =  <a href="xboole_0.html#K1">{}</a>  as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">O</font> <b>by </b><i><a class="ref" href="xboole_1.html#T2">XBOOLE_1:2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">tau</font> = <font color="Maroon">tau</font> as   <a href="struct_0.html#NM3">Subset-Family</a> of <font color="Maroon">O</font> ;<br/>
<b>take </b><font color="Maroon">Y</font> =  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">O</font>,<font color="Maroon">tau</font> #);<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_2_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:11_2_1_1"/>
<font color="Maroon">Y</font> is <a href="realset2.html#V3">trivial</a>
 ;<br/><a NAME="E2:11_2_1_1"/><b>then </b>
 ex <font color="Olive">d</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">Y</font> st 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="Olive">d</font></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E3:11_2_1_1"/>
contradiction
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E5:11_2_1"/>
( not <font color="Maroon">Y</font> is <a href="realset2.html#V3">trivial</a> &amp; <font color="Maroon">Y</font> is <a href="pre_topc.html#V1">strict</a> &amp; not <font color="Maroon">Y</font> is <a href="struct_0.html#V3">empty</a> )
 ;<br/>


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