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<b>let </b><font color="Maroon" title="c1">T1</font>, <font color="Maroon" title="c2">T2</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>

<b>assume </b><a NAME="E1:80"/><i><font color="Green" title="E49">A1</font></i>: 
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T1</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">T1</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T2</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c2">T2</font> #)
 ;<br/>

<a NAME="E2:80"/><i><font color="Green" title="E50">A2</font></i>: 
 <a href="yellow_6.html#K13" title="YELLOW_6:func.13">Convergence</a> <font color="Maroon" title="c1">T1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c1">T1</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T1</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D21" title="YELLOW_6:def.21">YELLOW_6:def 21</a></i>;<br/>
<a NAME="E3:80"/><i><font color="Green" title="E51">A3</font></i>: 
 <a href="yellow_6.html#K13" title="YELLOW_6:func.13">Convergence</a> <font color="Maroon" title="c2">T2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c2">T2</font></span>)</span>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T2</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_6.html#D21" title="YELLOW_6:def.21">YELLOW_6:def 21</a></i>;<br/>
<b>let </b><font color="Maroon" title="c3">u1</font>, <font color="Maroon" title="c4">u2</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="relat_1.html#D2" title="RELAT_1:def.2">RELAT_1:def 2</a><br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:80_1"/><i><font color="Green" title="E52">A4</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c4">u2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K13" title="YELLOW_6:func.13">Convergence</a> <font color="Maroon" title="c1">T1</font>
 ;<br/><b>then consider </b><font color="Maroon" title="c5">N1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c1">T1</font>, <font color="Maroon" title="c6">p1</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T1</font><b> such that </b><br/><a NAME="E3:80_1"/><i><font color="Green" title="E53">A5</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c4">u2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">N1</font>,<font color="Maroon" title="c6">p1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <b>by </b><i><a class="txt" href="waybel11.html#E2:80"><i><font color="Green" title="E50">A2</font></i></a>, <a class="ref" href="domain_1.html#T9" title="DOMAIN_1:th.9">DOMAIN_1:9</a></i>;<br/><a NAME="E4:80_1"/><i><font color="Green" title="E54">A6</font></i>: 
<font color="Maroon" title="c5">N1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c1">T1</font>
 ;<br/><a NAME="E5:80_1"/>
 ex <font color="Olive" title="b1">N</font> being <a href="waybel_0.html#V6" title="WAYBEL_0:attr.6">strict</a> <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">T1</font> st <br/>( <font color="Olive" title="b1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">N1</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K2" title="YELLOW_6:func.2">the_universe_of</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T1</font> )
 <b>by </b><i><a class="ref" href="yellow_6.html#D14" title="YELLOW_6:def.14">YELLOW_6:def 14</a></i>;<br/><b>then reconsider </b><font color="Maroon" title="c7">N1</font> = <font color="Maroon" title="c5">N1</font> as   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">T1</font> ;<br/><a NAME="E7:80_1"/><i><font color="Green" title="E55">A7</font></i>: 
<font color="Maroon" title="c6">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <font color="Maroon" title="c7">N1</font>
 <b>by </b><i><a class="txt" href="waybel11.html#E1:80_1"><i><font color="Green" title="E52">A4</font></i></a>, <a class="txt" href="waybel11.html#E3:80_1"><i><font color="Green" title="E53">A5</font></i></a>, <a class="ref" href="yellow_6.html#D22" title="YELLOW_6:def.22">YELLOW_6:def 22</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c8">N2</font> = <font color="Maroon" title="c7">N1</font> as   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c2">T2</font> <b>by </b><i><a class="txt" href="waybel11.html#E1:80"><i><font color="Green" title="E49">A1</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c9">p2</font> = <font color="Maroon" title="c6">p1</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">T2</font> <b>by </b><i><a class="txt" href="waybel11.html#E1:80"><i><font color="Green" title="E49">A1</font></i></a></i>;<br/><a NAME="E10:80_1"/>
( <font color="Maroon" title="c8">N2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c2">T2</font> &amp; <font color="Maroon" title="c9">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <font color="Maroon" title="c8">N2</font> )
 <b>by </b><i><a class="txt" href="waybel11.html#E1:80"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="waybel11.html#E4:80_1"><i><font color="Green" title="E54">A6</font></i></a>, <a class="txt" href="waybel11.html#E7:80_1"><i><font color="Green" title="E55">A7</font></i></a>, <a class="txt" href="waybel11.html#E54"><i><font color="Green" title="E45">Lm5</font></i></a>, <a class="txt" href="waybel11.html#E56"><i><font color="Green" title="E47">Lm7</font></i></a></i>;<br/><b>hence </b><a NAME="E11:80_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c4">u2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K13" title="YELLOW_6:func.13">Convergence</a> <font color="Maroon" title="c2">T2</font>
 <b>by </b><i><a class="txt" href="waybel11.html#E3:80_1"><i><font color="Green" title="E53">A5</font></i></a>, <a class="ref" href="yellow_6.html#D22" title="YELLOW_6:def.22">YELLOW_6:def 22</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E5:80"/><i><font color="Green" title="E52">A8</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c4">u2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K13" title="YELLOW_6:func.13">Convergence</a> <font color="Maroon" title="c2">T2</font>
 ;<br/>

<b>then consider </b><font color="Maroon" title="c5">N1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c2">T2</font>, <font color="Maroon" title="c6">p1</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">T2</font><b> such that </b><br/><a NAME="E7:80"/><i><font color="Green" title="E53">A9</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c4">u2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><span class="default"><font color="Maroon" title="c5">N1</font>,<font color="Maroon" title="c6">p1</font></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span>
 <b>by </b><i><a class="txt" href="waybel11.html#E3:80"><i><font color="Green" title="E51">A3</font></i></a>, <a class="ref" href="domain_1.html#T9" title="DOMAIN_1:th.9">DOMAIN_1:9</a></i>;<br/>
<a NAME="E8:80"/><i><font color="Green" title="E54">A10</font></i>: 
<font color="Maroon" title="c5">N1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c2">T2</font>
 
;<br/>
<a NAME="E9:80"/>
 ex <font color="Olive" title="b1">N</font> being <a href="waybel_0.html#V6" title="WAYBEL_0:attr.6">strict</a> <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c2">T2</font> st <br/>( <font color="Olive" title="b1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">N1</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">N</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K2" title="YELLOW_6:func.2">the_universe_of</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">T2</font> )
 
<b>by </b><i><a class="ref" href="yellow_6.html#D14" title="YELLOW_6:def.14">YELLOW_6:def 14</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c7">N1</font> = <font color="Maroon" title="c5">N1</font> as   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c2">T2</font> ;<br/>
<a NAME="E11:80"/><i><font color="Green" title="E55">A11</font></i>: 
<font color="Maroon" title="c6">p1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <font color="Maroon" title="c7">N1</font>
 
<b>by </b><i><a class="txt" href="waybel11.html#E5:80"><i><font color="Green" title="E52">A8</font></i></a>, <a class="txt" href="waybel11.html#E7:80"><i><font color="Green" title="E53">A9</font></i></a>, <a class="ref" href="yellow_6.html#D22" title="YELLOW_6:def.22">YELLOW_6:def 22</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">N2</font> = <font color="Maroon" title="c7">N1</font> as   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">T1</font> <b>by </b><i><a class="txt" href="waybel11.html#E1:80"><i><font color="Green" title="E49">A1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">p2</font> = <font color="Maroon" title="c6">p1</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T1</font> <b>by </b><i><a class="txt" href="waybel11.html#E1:80"><i><font color="Green" title="E49">A1</font></i></a></i>;<br/>
<a NAME="E14:80"/>
( <font color="Maroon" title="c8">N2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K7" title="YELLOW_6:func.7">NetUniv</a> <font color="Maroon" title="c1">T1</font> &amp; <font color="Maroon" title="c9">p2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K11" title="YELLOW_6:func.11">Lim</a> <font color="Maroon" title="c8">N2</font> )
 
<b>by </b><i><a class="txt" href="waybel11.html#E1:80"><i><font color="Green" title="E49">A1</font></i></a>, <a class="txt" href="waybel11.html#E8:80"><i><font color="Green" title="E54">A10</font></i></a>, <a class="txt" href="waybel11.html#E11:80"><i><font color="Green" title="E55">A11</font></i></a>, <a class="txt" href="waybel11.html#E54"><i><font color="Green" title="E45">Lm5</font></i></a>, <a class="txt" href="waybel11.html#E56"><i><font color="Green" title="E47">Lm7</font></i></a></i>;<br/>
<b>hence </b><a NAME="E15:80"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">u1</font>,<font color="Maroon" title="c4">u2</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow_6.html#K13" title="YELLOW_6:func.13">Convergence</a> <font color="Maroon" title="c1">T1</font>
 <b>by </b><i><a class="txt" href="waybel11.html#E7:80"><i><font color="Green" title="E53">A9</font></i></a>, <a class="ref" href="yellow_6.html#D22" title="YELLOW_6:def.22">YELLOW_6:def 22</a></i>;<br/>


</div>
