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<b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</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="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a>,<a class="ref" href="relat_2.html#D8" title="RELAT_2:def.8">RELAT_2:def 8</a><br/>

<b>assume </b><b>that </b><br/><a NAME="E1:27_1_1"/><i><font color="Green" title="E12">A1</font></i>: 
( <font color="Maroon" title="c2">x</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 <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">T</font></span>)</span> &amp; <font color="Maroon" title="c3">y</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 <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">T</font></span>)</span> &amp; <font color="Maroon" title="c4">z</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 <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">T</font></span>)</span> )
 <b>and </b><br/><a NAME="E2:27_1_1"/><i><font color="Green" title="E13">A2</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c3">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">T</font></span>)</span>
 <b>and </b><br/><a NAME="E3:27_1_1"/><i><font color="Green" title="E14">A3</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c3">y</font>,<font color="Maroon" title="c4">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">T</font></span>)</span>
 ;<br/>

<a NAME="E4:27_1_1"/><i><font color="Green" title="E15">A4</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 <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">T</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">T</font></span>)</span> #) <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="c1">T</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">T</font> #)
 
<b>by </b><i><a class="ref" href="waybel25.html#D2" target="_self" title="WAYBEL25:def.2">Def2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">a</font> = <font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c6">b</font> = <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c7">c</font> = <font color="Maroon" title="c4">z</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">T</font></span>)</span> <b>by </b><i><a class="txt" href="waybel25.html#E1:27_1_1"><i><font color="Green" title="E12">A1</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c8">t2</font> = <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c9">t3</font> = <font color="Maroon" title="c4">z</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">T</font> <b>by </b><i><a class="txt" href="waybel25.html#E1:27_1_1"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="waybel25.html#E4:27_1_1"><i><font color="Green" title="E15">A4</font></i></a></i>;<br/>
<a NAME="E7:27_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">b</font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E2:27_1_1"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c10">Y2</font> being   <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="E9:27_1_1"/><i><font color="Green" title="E16">A5</font></i>: 
<font color="Maroon" title="c10">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c6">b</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>and </b><br/><a NAME="E10:27_1_1"/><i><font color="Green" title="E17">A6</font></i>: 
<font color="Maroon" title="c5">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c10">Y2</font>
 <b>by </b><i><a class="ref" href="waybel25.html#D2" target="_self" title="WAYBEL25:def.2">Def2</a></i>;<br/>
<a NAME="E11:27_1_1"/>
<font color="Maroon" title="c6">b</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E3:27_1_1"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c11">Y3</font> being   <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="E13:27_1_1"/><i><font color="Green" title="E18">A7</font></i>: 
<font color="Maroon" title="c11">Y3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c7">c</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>and </b><br/><a NAME="E14:27_1_1"/><i><font color="Green" title="E19">A8</font></i>: 
<font color="Maroon" title="c6">b</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c11">Y3</font>
 <b>by </b><i><a class="ref" href="waybel25.html#D2" target="_self" title="WAYBEL25:def.2">Def2</a></i>;<br/>
<a NAME="E15:27_1_1"/>
( <font color="Maroon" title="c10">Y2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c8">t2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> &amp; <font color="Maroon" title="c11">Y3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c9">t3</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> )
 
<b>by </b><i><a class="txt" href="waybel25.html#E9:27_1_1"><i><font color="Green" title="E16">A5</font></i></a>, <a class="txt" href="waybel25.html#E13:27_1_1"><i><font color="Green" title="E18">A7</font></i></a></i>;<br/>
<a NAME="E16:27_1_1"/><b>then </b>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c10">Y2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c11">Y3</font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E14:27_1_1"><i><font color="Green" title="E19">A8</font></i></a>, <a class="txt" href="waybel25.html#E16"><i><font color="Green" title="E11">Lm2</font></i></a></i>;<br/>
<a NAME="E17:27_1_1"/><b>then </b>
<font color="Maroon" title="c5">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">c</font>
 
<b>by </b><i><a class="txt" href="waybel25.html#E10:27_1_1"><i><font color="Green" title="E17">A6</font></i></a>, <a class="txt" href="waybel25.html#E13:27_1_1"><i><font color="Green" title="E18">A7</font></i></a>, <a class="ref" href="waybel25.html#D2" target="_self" title="WAYBEL25:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E18:27_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c2">x</font>,<font color="Maroon" title="c4">z</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">T</font></span>)</span>
 <b>by </b><i><a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></i>;<br/>


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