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<div class="add">

<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>  st <font color="Maroon" title="c1">T</font> is <a href="urysohn1.html#V1" title="URYSOHN1:attr.1">being_T1</a> holds <br/> <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">T</font> is <a href="urysohn1.html#V1" title="URYSOHN1:attr.1">being_T1</a> implies  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font> )</span><br/>



<b>assume </b><a NAME="E1:43"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c1">T</font> is <a href="urysohn1.html#V1" title="URYSOHN1:attr.1">being_T1</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span><br/>

<b>let </b><font color="Maroon" title="c3">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span>)</span> or <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font> )</span><br/>

<b>assume </b><a NAME="E2:43"/><i><font color="Green" title="E26">A2</font></i>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c4">x'</font> = <font color="Maroon" title="c3">x</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font> ;<br/>
<b>assume </b><a NAME="E4:43"/>
not <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>then consider </b><font color="Maroon" title="c5">G</font> being  <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E6:43"/><i><font color="Green" title="E27">A3</font></i>: 
( <font color="Maroon" title="c4">x'</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">G</font> &amp; ( for <font color="Olive" title="b1">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>  holds <br/>(  not <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">G</font> or  not <font color="Maroon" title="c4">x'</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">y</font> ) ) )
 <b>by </b><i><a class="ref" href="topgen_1.html#T19" target="_self" title="TOPGEN_1:th.19">Th19</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c6">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E8:43"/><i><font color="Green" title="E28">A4</font></i>: 
( <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">G</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">y</font> )
 <b>by </b><i><a class="txt" href="topgen_1.html#E2:43"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="topgen_1.html#E6:43"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="topgen_1.html#T19" target="_self" title="TOPGEN_1:th.19">Th19</a></i>;<br/>
<a NAME="E9:43"/><i><font color="Green" title="E29">A5</font></i>: 
( <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">G</font> )
 
<b>by </b><i><a class="txt" href="topgen_1.html#E8:43"><i><font color="Green" title="E28">A4</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E10:43"/><b>then </b><i><font color="Green" title="E30">A6</font></i>: 
<font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E8:43"><i><font color="Green" title="E28">A4</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/>
<a NAME="E11:43"/><i><font color="Green" title="E31">A7</font></i>: 
<font color="Maroon" title="c5">G</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:43_1"/>
<font color="Maroon" title="c5">G</font> <a href="xboole_0.html#NR5" title="XBOOLE_0:NR.5">meets</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> contradiction</span><br/>

<b>then consider </b><font color="Maroon" title="c7">g</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:43_1"/><i><font color="Green" title="E32">A8</font></i>: 
( <font color="Maroon" title="c7">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">G</font> &amp; <font color="Maroon" title="c7">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>;<br/>
<a NAME="E4:43_1"/>
<font color="Maroon" title="c7">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E3:43_1"><i><font color="Green" title="E32">A8</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E5:43_1"/><b>then </b>
<font color="Maroon" title="c7">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c5">G</font>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E3:43_1"><i><font color="Green" title="E32">A8</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E6:43_1"/><b>then </b>
<font color="Maroon" title="c4">x'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">g</font>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E6:43"><i><font color="Green" title="E27">A3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:43_1"/>
contradiction
 <b>by </b><i><a class="txt" href="topgen_1.html#E3:43_1"><i><font color="Green" title="E32">A8</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c7">q</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E13:43"/><i><font color="Green" title="E32">A9</font></i>: 
( <font color="Maroon" title="c7">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">G</font> &amp; <font color="Maroon" title="c7">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 <b>by </b><i><a class="txt" href="topgen_1.html#E9:43"><i><font color="Green" title="E29">A5</font></i></a>, <a class="txt" href="topgen_1.html#E10:43"><i><font color="Green" title="E30">A6</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">q</font> = <font color="Maroon" title="c7">q</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font> <b>by </b><i><a class="txt" href="topgen_1.html#E13:43"><i><font color="Green" title="E32">A9</font></i></a></i>;<br/>
<a NAME="E15:43"/><i><font color="Green" title="E33">A10</font></i>: 
not <font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E13:43"><i><font color="Green" title="E32">A9</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E16:43"/><i><font color="Green" title="E34">A11</font></i>: 
<font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="topgen_1.html#K2" title="TOPGEN_1:func.2">Der</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E13:43"><i><font color="Green" title="E32">A9</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E17:43"/><i><font color="Green" title="E35">A12</font></i>: 
<font color="Maroon" title="c8">q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c3">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E13:43"><i><font color="Green" title="E32">A9</font></i></a>, <a class="txt" href="topgen_1.html#E15:43"><i><font color="Green" title="E33">A10</font></i></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</a></i>;<br/>
<a NAME="E18:43"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x'</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x'</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E1:43"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="yellow_8.html#T35" title="YELLOW_8:th.35">YELLOW_8:35</a></i>;<br/>
<a NAME="E19:43"/><b>then </b><i><font color="Green" title="E36">A13</font></i>: 
<font color="Maroon" title="c5">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x'</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 
<b>by </b><i><a class="ref" href="frechet.html#T4" title="FRECHET:th.4">FRECHET:4</a></i>;<br/>
<b>set </b><font color="Maroon" title="c9">U</font> = <font color="Maroon" title="c5">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x'</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>;<br/>
<b>consider </b><font color="Maroon" title="c10">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E21:43"/><i><font color="Green" title="E37">A14</font></i>: 
( <font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x'</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span></span>)</span> &amp; <font color="Maroon" title="c8">q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c10">y</font> )
 <b>by </b><i><a class="txt" href="topgen_1.html#E16:43"><i><font color="Green" title="E34">A11</font></i></a>, <a class="txt" href="topgen_1.html#E17:43"><i><font color="Green" title="E35">A12</font></i></a>, <a class="txt" href="topgen_1.html#E19:43"><i><font color="Green" title="E36">A13</font></i></a>, <a class="ref" href="topgen_1.html#T19" target="_self" title="TOPGEN_1:th.19">Th19</a></i>;<br/>
<a NAME="E22:43"/><i><font color="Green" title="E38">A15</font></i>: 
( <font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> &amp; <font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x'</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 
<b>by </b><i><a class="txt" href="topgen_1.html#E21:43"><i><font color="Green" title="E37">A14</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E23:43"/><b>then </b>
<font color="Maroon" title="c10">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">q</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E21:43"><i><font color="Green" title="E37">A14</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c11">f</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E25:43"/><i><font color="Green" title="E39">A16</font></i>: 
( <font color="Maroon" title="c11">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">G</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x'</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> &amp; <font color="Maroon" title="c11">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c8">q</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> )
 <b>by </b><i><a class="txt" href="topgen_1.html#E22:43"><i><font color="Green" title="E38">A15</font></i></a></i>;<br/>
<a NAME="E26:43"/><i><font color="Green" title="E40">A17</font></i>: 
( <font color="Maroon" title="c11">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">G</font> &amp; <font color="Maroon" title="c11">f</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">x'</font> )
 
<b>by </b><i><a class="txt" href="topgen_1.html#E25:43"><i><font color="Green" title="E39">A16</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/>
<a NAME="E27:43"/>
<font color="Maroon" title="c11">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E25:43"><i><font color="Green" title="E39">A16</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/>
<a NAME="E28:43"/><b>then </b>
<font color="Maroon" title="c11">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">A</font> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c4">x'</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 
<b>by </b><i><a class="txt" href="topgen_1.html#E26:43"><i><font color="Green" title="E40">A17</font></i></a>, <a class="ref" href="zfmisc_1.html#T64" title="ZFMISC_1:th.64">ZFMISC_1:64</a></i>;<br/>
<b>hence </b><a NAME="E29:43"/>
contradiction
 <b>by </b><i><a class="txt" href="topgen_1.html#E11:43"><i><font color="Green" title="E31">A7</font></i></a>, <a class="txt" href="topgen_1.html#E26:43"><i><font color="Green" title="E40">A17</font></i></a>, <a class="ref" href="xboole_0.html#T3" title="XBOOLE_0:th.3">XBOOLE_0:3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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