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<div class="add">

<a NAME="E1:21"/>
for <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="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span> holds <span class="p1">(<span class="default"><a href="treal_1.html#K4" target="_self">P[01]</a> 0,1,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span>;<br/>

<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> = <font color="Maroon">c<sub>1</sub></font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="txt" href="treal_1.html#E6"><i><font color="Green">Lemma6</font></i></a></i>;<br/>
<a NAME="E2:21_1"/>
(  <a href="treal_1.html#K1" target="_self">(#)</a> 0,1 <a href="hidden.html#R1">=</a> 0 &amp; 0,1 <a href="treal_1.html#K2" target="_self">(#)</a>  <a href="hidden.html#R1">=</a> 1 )
 
<b>by </b><i><a class="ref" href="treal_1.html#D1" target="_self">Def1</a>, <a class="ref" href="treal_1.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><a href="treal_1.html#K4" target="_self">P[01]</a> 0,1,<span class="p2">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span>,<span class="p2">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span></span>)</span> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">1 <a href="real_1.html#K5">-</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="real_1.html#K4">*</a> 0</span>)</span> <a href="real_1.html#K3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="real_1.html#K5">-</a> 0</span>)</span> <a href="real_1.html#K4">*</a> 1</span>)</span></span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K5">-</a> 0</span>)</span>
<b>by </b><i><a class="ref" href="treal_1.html#D4" target="_self">Def4</a></i>
<br/>.= 
<font color="Maroon">c<sub>1</sub></font>

;<br/><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:21"/>
 <a href="treal_1.html#K4" target="_self">P[01]</a> 0,1,<span class="p1">(<span class="default"><a href="treal_1.html#K1" target="_self">(#)</a> 0,1</span>)</span>,<span class="p1">(<span class="default">0,1 <a href="treal_1.html#K2" target="_self">(#)</a> </span>)</span> <a href="funct_2.html#R2">=</a>  <a href="grcat_1.html#K7">id</a> <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span>
 <b>by </b><i><a class="ref" href="tmap_1.html#T92">TMAP_1:92</a></i>;<br/>


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