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<b>let </b><font color="Maroon">a</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> , <font color="Maroon">b</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><a NAME="E1:31"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 ;<br/>

<b>set </b><font color="Maroon">f</font> =  <a href="jordan16.html#K1" target="_self">AffineMap</a> <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/>
<b>let </b><font color="Maroon">x1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">x2</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="funct_1.html#D8">FUNCT_1:def 8</a><br/>

<b>assume </b><a NAME="E2:31"/>
<font color="Maroon">x1</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="jordan16.html#K1" target="_self">AffineMap</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">r1</font> = <font color="Maroon">x1</font> as  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<b>assume </b><a NAME="E4:31"/>
<font color="Maroon">x2</font> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="jordan16.html#K1" target="_self">AffineMap</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">r2</font> = <font color="Maroon">x2</font> as  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>  <b>by </b><i><a class="ref" href="xreal_0.html#D1">XREAL_0:def 1</a></i>;<br/>
<b>assume </b><a NAME="E6:31"/>
<span class="p1">(<span class="default"><a href="jordan16.html#K1" target="_self">AffineMap</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="jordan16.html#K1" target="_self">AffineMap</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font>
 ;<br/>

<b>then </b><span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r1</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font> = 
<span class="p1">(<span class="default"><a href="jordan16.html#K1" target="_self">AffineMap</a> <font color="Maroon">a</font>,<font color="Maroon">b</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x2</font>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r2</font></span>)</span> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">b</font>
<b>by </b><i/>
;<br/>
<a NAME="E8:31"/><b>then </b>
<font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">a</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">r2</font>
 
;<br/>
<b>hence </b><a NAME="E9:31"/>
<font color="Maroon">x1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">x2</font>
 <b>by </b><i>, <a class="ref" href="xcmplx_1.html#T5">XCMPLX_1:5</a></i>;<br/>


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