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<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_2.html#K2">REAL+</a> ;<br/><b>let </b><font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_2.html#K2">REAL+</a> ;<br/>



<b>assume </b><a NAME="E1:3"/><i><font color="Green">E15</font></i>: 
<font color="Maroon">x</font> <a href="arytm_2.html#K8">*'</a> <font color="Maroon">y</font> <a href="hidden.html#R1">=</a>  <a href="arytm_3.html#K13">{}</a> 
 ;<br/>

<b>assume </b><a NAME="E2:3"/>
<font color="Maroon">x</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="arytm_3.html#K13">{}</a> 
 ;<br/>

<b>then consider </b><font color="Maroon">x1</font> being    <a href="subset_1.html#M1">Element</a> of  <a href="arytm_2.html#K2">REAL+</a> <b> such that </b><br/><a NAME="E4:3"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">x</font> <a href="arytm_2.html#K8">*'</a> <font color="Maroon">x1</font> <a href="hidden.html#R1">=</a>  <a href="arytm_3.html#K14">one</a> 
 <b>by </b><i><a class="ref" href="arytm_2.html#T15">ARYTM_2:15</a></i>;<br/>
<b>thus </b><font color="Maroon">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="arytm_2.html#K8">*'</a> <font color="Maroon">x1</font></span>)</span> <a href="arytm_2.html#K8">*'</a> <font color="Maroon">y</font>
<b>by </b><i>, <a class="ref" href="arytm_2.html#T16">ARYTM_2:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="arytm_2.html#K8">*'</a> <font color="Maroon">y</font></span>)</span> <a href="arytm_2.html#K8">*'</a> <font color="Maroon">x1</font>
<b>by </b><i><a class="ref" href="arytm_2.html#T13">ARYTM_2:13</a></i>
<br/>.= 
 <a href="arytm_3.html#K13">{}</a> 
<b>by </b><i>, <a class="ref" href="arytm_2.html#T4">ARYTM_2:4</a></i>
;<br/>


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