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

<b>let </b><font color="Maroon">c<sub>39</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span>;<br/>

<b>assume </b><a NAME="E1:105"/><i><font color="Green">E84</font></i>: 
<font color="Maroon">c<sub>39</sub></font> <a href="hidden.html#R1">=</a>  <a href="toprealb.html#K10" target="_self">c[-10]</a> 
 ;<br/>

<b>set </b><font color="Maroon">c<sub>40</sub></font> = <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  ) </span>}</span> ;<br/>
<b>set </b><font color="Maroon">c<sub>41</sub></font> = <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> &amp; 0 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  ) </span>}</span> ;<br/>
<a NAME="E2:105"/><i><font color="Green">E85</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  ) </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>42</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:105_1"/>
<font color="Maroon">c<sub>42</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  ) </span>}</span> 
 ;<br/>

<a NAME="E2:105_1"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> st <br/>( <font color="Maroon">c<sub>42</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  )
 
;<br/>
<b>hence </b><a NAME="E3:105_1"/>
<font color="Maroon">c<sub>42</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E3:105"/><i><font color="Green">E86</font></i>: 
<span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> &amp; 0 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  ) </span>}</span>  <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>42</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:105_2"/>
<font color="Maroon">c<sub>42</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> &amp; 0 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  ) </span>}</span> 
 ;<br/>

<a NAME="E2:105_2"/><b>then </b>
ex <font color="Olive">b<sub>1</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> st <br/>( <font color="Maroon">c<sub>42</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> &amp; 0 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  )
 
;<br/>
<b>hence </b><a NAME="E3:105_2"/>
<font color="Maroon">c<sub>42</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span>
 ;<br/>


</div><b>end;</b></div>
<b>reconsider </b><font color="Maroon">c<sub>42</sub></font> =  <a href="toprealb.html#K10" target="_self">c[-10]</a>  as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> ;<br/>
<a NAME="E5:105"/><i><font color="Green">E87</font></i>: 
<font color="Maroon">c<sub>42</sub></font> <a href="euclid.html#K22">`2</a>  <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="euclid.html#T56">EUCLID:56</a></i>;<br/>
<a NAME="E6:105"/>
 <a href="toprealb.html#K10" target="_self">c[-10]</a>  is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="toprealb.html#T21" target="_self">Th21</a>, <a class="ref" href="toprealb.html#T24" target="_self">Th24</a></i>;<br/>
<a NAME="E7:105"/><b>then </b><i><font color="Green">E88</font></i>: 
(  <a href="toprealb.html#K10" target="_self">c[-10]</a>  <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  ) </span>}</span>  &amp;  <a href="toprealb.html#K10" target="_self">c[-10]</a>  <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> &amp; 0 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  ) </span>}</span>  )
 
<b>by </b><i><a class="txt" href="toprealb.html#E5:105"><i><font color="Green">E87</font></i></a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>43</sub></font> = <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> &amp; 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  ) </span>}</span> , <font color="Maroon">c<sub>44</sub></font> = <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> : ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> &amp; 0 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Olive">b<sub>1</sub></font> <a href="euclid.html#K22">`2</a>  ) </span>}</span>  as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <b>by </b><i><a class="txt" href="toprealb.html#E2:105"><i><font color="Green">E85</font></i></a>, <a class="txt" href="toprealb.html#E3:105"><i><font color="Green">E86</font></i></a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>45</sub></font> = <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>43</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>46</sub></font> = <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>44</sub></font>;<br/>
<a NAME="E9:105"/><i><font color="Green">E89</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>43</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>43</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>47</sub></font> = <font color="Maroon">c<sub>39</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>43</sub></font></span>)</span> <b>by </b><i><a class="txt" href="toprealb.html#E1:105"><i><font color="Green">E84</font></i></a>, <a class="txt" href="toprealb.html#E7:105"><i><font color="Green">E88</font></i></a>, <a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E11:105"/><i><font color="Green">E90</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>44</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>44</sub></font>
 
<b>by </b><i><a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>48</sub></font> = <font color="Maroon">c<sub>39</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>44</sub></font></span>)</span> <b>by </b><i><a class="txt" href="toprealb.html#E1:105"><i><font color="Green">E84</font></i></a>, <a class="txt" href="toprealb.html#E7:105"><i><font color="Green">E88</font></i></a>, <a class="ref" href="pre_topc.html#T29">PRE_TOPC:29</a></i>;<br/>
<a NAME="E13:105"/><i><font color="Green">E91</font></i>: 
 <a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a>  is    <a href="pre_topc.html#M1">SubSpace</a> of  <a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> 
 
<b>by </b><i><a class="ref" href="tsep_1.html#T2">TSEP_1:2</a></i>;<br/>
<a NAME="E14:105"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>43</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>44</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_3"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:105_3"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>43</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>44</sub></font>
  <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="105_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>49</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E1:105_3_1"/><i><font color="Green">E92</font></i>: 
<font color="Maroon">c<sub>49</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>50</sub></font> = <font color="Maroon">c<sub>49</sub></font> as   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15">TOP-REAL</a> 2</span>)</span> <b>by </b><i><a class="txt" href="toprealb.html#E11"><i><font color="Green">Lemma9</font></i></a></i>;<br/>
<a NAME="E3:105_3_1"/>
( 0 <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="euclid.html#K22">`2</a>  or 0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>50</sub></font> <a href="euclid.html#K22">`2</a>  )
 
;<br/>
<a NAME="E4:105_3_1"/><b>then </b>
( <font color="Maroon">c<sub>50</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>43</sub></font> or <font color="Maroon">c<sub>50</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>44</sub></font> )
 
<b>by </b><i><a class="txt" href="toprealb.html#E1:105_3_1"><i><font color="Green">E92</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:105_3_1"/>
<font color="Maroon">c<sub>49</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>43</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>44</sub></font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E2:105_3"/>
<font color="Maroon">c<sub>43</sub></font> <a href="subset_1.html#K4">\/</a> <font color="Maroon">c<sub>44</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E15:105"/><b>then </b><i><font color="Green">E92</font></i>: 
 <a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>43</sub></font></span>)</span> <a href="tsep_1.html#K1">union</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>44</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="toprealb.html#E9:105"><i><font color="Green">E89</font></i></a>, <a class="txt" href="toprealb.html#E11:105"><i><font color="Green">E90</font></i></a>, <a class="txt" href="toprealb.html#E13:105"><i><font color="Green">E91</font></i></a>, <a class="ref" href="tsep_1.html#D2">TSEP_1:def 2</a></i>;<br/>
<a NAME="E16:105"/>
<a href="toprealb.html#K14" target="_self">Circle2IntervalR</a>  <a href="tmap_1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>43</sub></font></span>)</span> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="toprealb.html#E124"><i><font color="Green">Lemma81</font></i></a></i>;<br/>
<a NAME="E17:105"/><b>then </b><i><font color="Green">E93</font></i>: 
<a href="toprealb.html#K14" target="_self">Circle2IntervalR</a>  <a href="tmap_1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>43</sub></font></span>)</span> <a href="tmap_1.html#R1">is_continuous_at</a> <font color="Maroon">c<sub>47</sub></font>
 
<b>by </b><i><a class="ref" href="tmap_1.html#T49">TMAP_1:49</a></i>;<br/>
<a NAME="E18:105"/>
<a href="toprealb.html#K14" target="_self">Circle2IntervalR</a>  <a href="tmap_1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>44</sub></font></span>)</span> is <a href="pre_topc.html#V5">continuous</a>
 
<b>by </b><i><a class="txt" href="toprealb.html#E125"><i><font color="Green">Lemma82</font></i></a></i>;<br/>
<a NAME="E19:105"/><b>then </b>
<a href="toprealb.html#K14" target="_self">Circle2IntervalR</a>  <a href="tmap_1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="toprealb.html#K11" target="_self">Topen_unit_circle</a> <a href="toprealb.html#K9" target="_self">c[10]</a> </span>)</span> <a href="pre_topc.html#K3">|</a> <font color="Maroon">c<sub>44</sub></font></span>)</span> <a href="tmap_1.html#R1">is_continuous_at</a> <font color="Maroon">c<sub>48</sub></font>
 
<b>by </b><i><a class="ref" href="tmap_1.html#T49">TMAP_1:49</a></i>;<br/>
<b>hence </b><a NAME="E20:105"/>
 <a href="toprealb.html#K14" target="_self">Circle2IntervalR</a>  <a href="tmap_1.html#R1">is_continuous_at</a> <font color="Maroon">c<sub>39</sub></font>
 <b>by </b><i><a class="txt" href="toprealb.html#E15:105"><i><font color="Green">E92</font></i></a>, <a class="txt" href="toprealb.html#E17:105"><i><font color="Green">E93</font></i></a>, <a class="ref" href="tmap_1.html#T125">TMAP_1:125</a></i>;<br/>


</div>
