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

<b>set </b><font color="Maroon">G</font> =  <a href="group_1.html#G1" target="_self">HGrStr</a>(# <a href="numbers.html#K1">REAL</a> ,<a href="binop_2.html#K33">addreal</a>  #);<br/>
<a NAME="E1:11"/><i><font color="Green">E40</font></i>: 
for <font color="Olive">h</font>, <font color="Olive">g</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="group_1.html#G1" target="_self">HGrStr</a>(# <a href="numbers.html#K1">REAL</a> ,<a href="binop_2.html#K33">addreal</a>  #)<br/> for <font color="Olive">A</font>, <font color="Olive">B</font> being  <a href="real_1.html#NM1">Real</a>  st <font color="Olive">h</font> <a href="hidden.html#R1">=</a> <font color="Olive">A</font> &amp; <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Olive">B</font> holds <br/><font color="Olive">h</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Olive">g</font> <a href="hidden.html#R1">=</a> <font color="Olive">A</font> <a href="binop_2.html#K9">+</a> <font color="Olive">B</font>
 
<b>by </b><i><a class="ref" href="binop_2.html#D9">BINOP_2:def 9</a></i>;<br/>
<b>thus </b><a NAME="E2:11"/>
for <font color="Olive">h</font>, <font color="Olive">g</font>, <font color="Olive">f</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="group_1.html#G1" target="_self">HGrStr</a>(# <a href="numbers.html#K1">REAL</a> ,<a href="binop_2.html#K33">addreal</a>  #) holds  <span class="p1">(<span class="default"><font color="Olive">h</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Olive">g</font></span>)</span> <a href="group_1.html#K1" target="_self">*</a> <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Olive">h</font> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Olive">g</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Olive">f</font></span>)</span>
  <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D4" target="_self">GROUP_1:def 4</a><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="11_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">h</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="group_1.html#G1" target="_self">HGrStr</a>(# <a href="numbers.html#K1">REAL</a> ,<a href="binop_2.html#K33">addreal</a>  #), <font color="Maroon">g</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="group_1.html#G1" target="_self">HGrStr</a>(# <a href="numbers.html#K1">REAL</a> ,<a href="binop_2.html#K33">addreal</a>  #), <font color="Maroon">f</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="group_1.html#G1" target="_self">HGrStr</a>(# <a href="numbers.html#K1">REAL</a> ,<a href="binop_2.html#K33">addreal</a>  #);<br/>

<b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">h</font>, <font color="Maroon">B</font> = <font color="Maroon">g</font>, <font color="Maroon">C</font> = <font color="Maroon">f</font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<a NAME="E2:11_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">h</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">g</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> <a href="binop_2.html#K9">+</a> <font color="Maroon">B</font>
 
<b>by </b><i/>;<br/>
<a NAME="E3:11_1"/><i><font color="Green">E47</font></i>: 
<font color="Maroon">g</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B</font> <a href="binop_2.html#K9">+</a> <font color="Maroon">C</font>
 
<b>by </b><i/>;<br/>
<b>thus </b><span class="p1">(<span class="default"><font color="Maroon">h</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">g</font></span>)</span> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">f</font> = 
<span class="p1">(<span class="default"><font color="Maroon">A</font> <a href="binop_2.html#K9">+</a> <font color="Maroon">B</font></span>)</span> <a href="binop_2.html#K9">+</a> <font color="Maroon">C</font>
<b>by </b><i>, </i>
<br/>.= 
<font color="Maroon">A</font> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><font color="Maroon">B</font> <a href="binop_2.html#K9">+</a> <font color="Maroon">C</font></span>)</span>

<br/>.= 
<font color="Maroon">h</font> <a href="group_1.html#K1" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">f</font></span>)</span>
<b>by </b><i>, </i>
;<br/>


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

<b>reconsider </b><font color="Maroon">e</font> = 0 as   <a href="struct_0.html#NM1">Element</a> of <a href="group_1.html#G1" target="_self">HGrStr</a>(# <a href="numbers.html#K1">REAL</a> ,<a href="binop_2.html#K33">addreal</a>  #) ;<br/>
<b>take </b>
<font color="Maroon">e</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="group_1.html#D3" target="_self">GROUP_1:def 3</a><br/>

<b>let </b><font color="Maroon">h</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="group_1.html#G1" target="_self">HGrStr</a>(# <a href="numbers.html#K1">REAL</a> ,<a href="binop_2.html#K33">addreal</a>  #);<br/>

<b>reconsider </b><font color="Maroon">A</font> = <font color="Maroon">h</font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<b>thus </b><font color="Maroon">h</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">e</font> = 
<font color="Maroon">A</font> <a href="binop_2.html#K9">+</a> 0
<b>by </b><i/>
<br/>.= 
<font color="Maroon">h</font>

;<br/>

<b>thus </b><font color="Maroon">e</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">h</font> = 
0 <a href="binop_2.html#K9">+</a> <font color="Maroon">A</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">h</font>

;<br/>

<b>reconsider </b><font color="Maroon">g</font> =  <a href="binop_2.html#K7">-</a> <font color="Maroon">A</font> as   <a href="struct_0.html#NM1">Element</a> of <a href="group_1.html#G1" target="_self">HGrStr</a>(# <a href="numbers.html#K1">REAL</a> ,<a href="binop_2.html#K33">addreal</a>  #) ;<br/>
<b>take </b>
<font color="Maroon">g</font>
;<br/>

<b>thus </b><font color="Maroon">h</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">g</font> = 
<font color="Maroon">A</font> <a href="binop_2.html#K9">+</a> <span class="p1">(<span class="default"><a href="binop_2.html#K7">-</a> <font color="Maroon">A</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">e</font>

;<br/>

<b>thus </b><font color="Maroon">g</font> <a href="group_1.html#K1" target="_self">*</a> <font color="Maroon">h</font> = 
<span class="p1">(<span class="default"><a href="binop_2.html#K7">-</a> <font color="Maroon">A</font></span>)</span> <a href="binop_2.html#K9">+</a> <font color="Maroon">A</font>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">e</font>

;<br/>


</div>
