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<a NAME="E1:47_1_1"/><i><font color="Green" title="E35">A1</font></i>: 
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">S</font>
 
<b>by </b><i><a class="ref" href="pencil_1.html#D5" title="PENCIL_1:def.5">PENCIL_1:def 5</a></i>;<br/>
<b>assume </b><a NAME="E2:47_1_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pencil_4.html#K11" title="PENCIL_4:func.11">VeroneseSpace</a> <font color="Maroon" title="c1">S</font></span>)</span> is   <a href="pencil_1.html#NM1" title="PENCIL_1:NM.1">Block</a> of <span class="p1">(<span class="default"><a href="pencil_4.html#K11" title="PENCIL_4:func.11">VeroneseSpace</a> <font color="Maroon" title="c1">S</font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_1.html#D5" title="PENCIL_1:def.5">PENCIL_1:def 5</a><br/>

<b>then consider </b><font color="Maroon" title="c2">t</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> , <font color="Maroon" title="c3">l</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font><b> such that </b><br/><a NAME="E4:47_1_1"/><i><font color="Green" title="E36">A2</font></i>: 
( <font color="Maroon" title="c2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> &amp; <font color="Maroon" title="c3">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">S</font> &amp;  <a href="pencil_4.html#K8" title="PENCIL_4:func.8">PairSet</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pencil_4.html#K9" title="PENCIL_4:func.9">PairSet</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c3">l</font> )
 <b>by </b><i><a class="ref" href="pencil_4.html#D10" target="_self" title="PENCIL_4:def.10">Def10</a></i>;<br/>
<a NAME="E5:47_1_1"/>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">l</font>
 
<b>by </b><i><a class="txt" href="pencil_4.html#E1:47_1_1"><i><font color="Green" title="E35">A1</font></i></a>, <a class="txt" href="pencil_4.html#E4:47_1_1"><i><font color="Green" title="E36">A2</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c4">s</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E7:47_1_1"/><i><font color="Green" title="E37">A3</font></i>: 
( <font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> &amp; not <font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">l</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="47_1_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:47_1_1_1"/>
<span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c4">s</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pencil_4.html#K9" title="PENCIL_4:func.9">PairSet</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c3">l</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c5">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:47_1_1_1"/><i><font color="Green" title="E38">A4</font></i>: 
( <font color="Maroon" title="c5">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">l</font> &amp; <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c4">s</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c5">z</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <b>by </b><i><a class="ref" href="pencil_4.html#D9" target="_self" title="PENCIL_4:def.9">Def9</a></i>;<br/><a NAME="E4:47_1_1_1"/>
<font color="Maroon" title="c4">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t</font>
 <b>by </b><i><a class="txt" href="pencil_4.html#E7:47_1_1"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="pencil_4.html#E3:47_1_1_1"><i><font color="Green" title="E38">A4</font></i></a>, <a class="ref" href="zfmisc_1.html#T10" title="ZFMISC_1:th.10">ZFMISC_1:10</a></i>;<br/><b>hence </b><a NAME="E5:47_1_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="pencil_4.html#E7:47_1_1"><i><font color="Green" title="E37">A3</font></i></a>, <a class="txt" href="pencil_4.html#E3:47_1_1_1"><i><font color="Green" title="E38">A4</font></i></a>, <a class="ref" href="zfmisc_1.html#T10" title="ZFMISC_1:th.10">ZFMISC_1:10</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:47_1_1"/>
contradiction
 <b>by </b><i><a class="txt" href="pencil_4.html#E4:47_1_1"><i><font color="Green" title="E36">A2</font></i></a>, <a class="txt" href="pencil_4.html#E7:47_1_1"><i><font color="Green" title="E37">A3</font></i></a>, <a class="ref" href="pencil_4.html#D8" target="_self" title="PENCIL_4:def.8">Def8</a></i>;<br/>


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