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<b>let </b><font color="Maroon">F1</font> be   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span>, <font color="Maroon">F2</font> be   <a href="struct_0.html#NM6">Function</a> of <span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>,<span class="p1">(<span class="default"><a href="topmetr.html#K4">Closed-Interval-TSpace</a> 0,1</span>)</span>;<br/>

<b>assume </b><a NAME="E1:14_1_2"/><i><font color="Green">E77</font></i>: 
for <font color="Olive">s</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> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span><br/> for <font color="Olive">r</font>, <font color="Olive">r1</font>, <font color="Olive">r2</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Olive">r</font> &amp; <font color="Olive">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t1</font> &amp; <font color="Olive">r2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t2</font> holds <br/><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">r</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">r1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">r</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
 ;<br/>

<b>assume </b><a NAME="E2:14_1_2"/><i><font color="Green">E91</font></i>: 
for <font color="Olive">s</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> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span><br/> for <font color="Olive">r</font>, <font color="Olive">r1</font>, <font color="Olive">r2</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Olive">r</font> &amp; <font color="Olive">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t1</font> &amp; <font color="Olive">r2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">t2</font> holds <br/><font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Olive">r</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">r1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">r</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Olive">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
 ;<br/>

<a NAME="E3:14_1_2"/>
for <font color="Olive">s</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> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> holds  <font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Olive">s</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Olive">s</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">s</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> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>;<br/>

<b>reconsider </b><font color="Maroon">r</font> = <font color="Maroon">s</font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i>, </i>;<br/>
<b>reconsider </b><font color="Maroon">r1</font> = <font color="Maroon">t1</font>, <font color="Maroon">r2</font> = <font color="Maroon">t2</font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i/>;<br/>
<b>thus </b><font color="Maroon">F1</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">r</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">r</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r2</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K6">-</a> <font color="Maroon">a</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">F2</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">s</font>
<b>by </b><i/>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:14_1_2"/>
<font color="Maroon">F1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">F2</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113">FUNCT_2:113</a></i>;<br/>


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