<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V2">Lawson</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be  <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V2">Lawson</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:33"/><i><font color="Green">E17</font></i>: 
 <a href="yellow_1.html#K2">InclPoset</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> is <a href="waybel_3.html#V3">continuous</a>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V2">Lawson</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V1">lower</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V2">correct</a> <a href="waybel11.html#V4">Scott</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span>;<br/>
<a NAME="E5:33"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is    <a href="yellow_9.html#M3">Refinement</a> of <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="waybel19.html#T29">WAYBEL19:29</a></i>;<br/>
<a NAME="E6:33"/>
<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font> #)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">c<sub>8</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V2">correct</a> <a href="waybel11.html#V4">Scott</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>9</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V2">correct</a> <a href="waybel11.html#V4">Scott</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V1">lower</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>consider </b><font color="Maroon">c<sub>11</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#V2">correct</a> <a href="waybel19.html#V1">lower</a>  <a href="yellow_9.html#M1">TopAugmentation</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E5:33_1"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> is    <a href="yellow_9.html#M3">Refinement</a> of <font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> is    <a href="yellow_9.html#M3">Refinement</a> of <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="ref" href="waybel19.html#T29">WAYBEL19:29</a></i>;<br/>
<a NAME="E6:33_1"/><i><font color="Green">E20</font></i>: 
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>8</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) &amp;  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>9</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>9</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #) &amp;  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>10</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>10</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) &amp;  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>11</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>11</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #) )
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<a NAME="E7:33_1"/><i><font color="Green">E21</font></i>: 
(  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>3</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) &amp;  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>4</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #) )
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<a NAME="E8:33_1"/><i><font color="Green">E22</font></i>: 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>5</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span> #)
 
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>;<br/>
<i><font color="Green">E23</font></i>: the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> = 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="ref" href="borsuk_1.html#D5">BORSUK_1:def 5</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="waybel30.html#E7:33_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="waybel30.html#E8:33_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="yellow_3.html#D2">YELLOW_3:def 2</a></i>
;<br/>
<a NAME="E10:33_1"/>
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font> #) is    <a href="yellow_9.html#M3">Refinement</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="borsuk_1.html#K5">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="borsuk_1.html#K5">:]</a></span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_2"><b>proof </b></a><div class="add">

<a NAME="E1:33_1_2"/>
<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> is    <a href="yellow_9.html#M3">Refinement</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="borsuk_1.html#K5">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="borsuk_1.html#K5">:]</a></span>
 
<b>by </b><i><a class="txt" href="waybel30.html#E5:33_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="waybel30.html#E6:33_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="yellow12.html#T50">YELLOW12:50</a></i>;<br/>
<b>hence </b><a NAME="E2:33_1_2"/>
the <a href="struct_0.html#U1">carrier</a> of <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font> #) <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="xboole_0.html#K2">\/</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="borsuk_1.html#K5">:]</a></span>
 <b>by </b><i><a class="txt" href="waybel30.html#E9:33_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="yellow_9.html#D6">YELLOW_9:def 6</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_9.html#D6">YELLOW_9:def 6</a><br/>

<a NAME="E3:33_1_2"/><i><font color="Green">E24</font></i>: 
<span class="p1">(<span class="default"><a href="waybel19.html#K1">omega</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> is    <a href="cantor_1.html#M2">prebasis</a> of <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="waybel19.html#D3">WAYBEL19:def 3</a></i>;<br/>
<i><font color="Green">E25</font></i>: the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> = 
 <a href="waybel19.html#K1">omega</a> <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span>
<b>by </b><i><a class="ref" href="waybel19.html#T15">WAYBEL19:15</a></i>
<br/>.= 
 <a href="waybel19.html#K1">omega</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="waybel30.html#E8:33_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="waybel19.html#T3">WAYBEL19:3</a></i>
;<br/>
<i><font color="Green">E26</font></i>:  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>9</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>9</sub></font> #) = 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #)
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>
<br/>.= 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1">Sigma</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1">Sigma</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> #)
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>
;<br/>
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>8</sub></font> #) = 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #)
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>
<br/>.= 
 <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,the <a href="orders_2.html#U1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #)
<b>by </b><i><a class="ref" href="yellow_9.html#D4">YELLOW_9:def 4</a></i>
;<br/>
<a NAME="E7:33_1_2"/><b>then </b>
(  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>9</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>9</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1">Sigma</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1">Sigma</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> #) &amp;  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>8</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) )
 
<b>by </b><i><a class="txt" href="waybel30.html#E5:33_1_2"><i><font color="Green">E26</font></i></a>, <a class="ref" href="waybel29.html#T17">WAYBEL29:17</a></i>;<br/>
<b>then </b>the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> = 
the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel29.html#K1">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel29.html#K1">Sigma</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span>
<b>by </b><i><a class="ref" href="waybel29.html#T10">WAYBEL29:10</a></i>
<br/>.= 
 <a href="waybel11.html#K5">sigma</a> <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span>
<b>by </b><i><a class="txt" href="waybel30.html#E1:33"><i><font color="Green">E17</font></i></a>, <a class="ref" href="waybel29.html#T34">WAYBEL29:34</a></i>
<br/>.= 
 <a href="waybel11.html#K5">sigma</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="waybel30.html#E8:33_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="yellow_9.html#T52">YELLOW_9:52</a></i>
;<br/>
<b>hence </b><a NAME="E9:33_1_2"/>
the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="xboole_0.html#K2">\/</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> is    <a href="cantor_1.html#M2">prebasis</a> of  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font> #)
 <b>by </b><i><a class="txt" href="waybel30.html#E3:33_1_2"><i><font color="Green">E24</font></i></a>, <a class="txt" href="waybel30.html#E4:33_1_2"><i><font color="Green">E25</font></i></a>, <a class="ref" href="yellow12.html#T33">YELLOW12:33</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E11:33_1"/>
<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font>,the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>5</sub></font> #)
 <b>by </b><i><a class="txt" href="waybel30.html#E5:33_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="waybel30.html#E6:33_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="waybel30.html#E9:33_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="yellow12.html#T49">YELLOW12:49</a></i>;<br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> as    <a href="yellow_9.html#M3">Refinement</a> of <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font> <b>by </b><i><a class="txt" href="waybel30.html#E5:33"><i><font color="Green">E18</font></i></a>, <a class="ref" href="yellow12.html#T47">YELLOW12:47</a></i>;<br/>
<a NAME="E8:33"/>
the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">c<sub>8</sub></font>
 
;<br/>
<b>hence </b><a NAME="E9:33"/>
the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="waybel19.html#K2">lambda</a> <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3">:]</a></span>
 <b>by </b><i><a class="ref" href="waybel19.html#T34">WAYBEL19:34</a></i>;<br/>


</div>
