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<b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font>, <font color="Maroon" title="c4">z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c4">z</font> &amp; <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  implies <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">z</font> )</span><br/>





<b>assume </b><a NAME="E1:2"/><i><font color="Green" title="E3">A1</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c4">z</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a>  or <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">z</font> )</span><br/>

<b>assume </b><a NAME="E2:2"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="arytm_3.html#K11" title="ARYTM_3:func.11">{}</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">z</font></span><br/>

<b>then consider </b><font color="Maroon" title="c5">x1</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="arytm_2.html#K2" title="ARYTM_2:func.2">REAL+</a> <b> such that </b><br/><a NAME="E4:2"/><i><font color="Green" title="E4">A2</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c5">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="arytm_3.html#K12" title="ARYTM_3:func.12">one</a> 
 <b>by </b><i><a class="ref" href="arytm_2.html#T15" title="ARYTM_2:th.15">ARYTM_2:15</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c3">y</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c3">y</font>
<b>by </b><i><a class="txt" href="arytm_1.html#E4:2"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="arytm_2.html#T16" title="ARYTM_2:th.16">ARYTM_2:16</a></i>
<br/>.= 
<font color="Maroon" title="c5">x1</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c4">z</font></span>)</span>
<b>by </b><i><a class="txt" href="arytm_1.html#E1:2"><i><font color="Green" title="E3">A1</font></i></a>, <a class="ref" href="arytm_2.html#T13" title="ARYTM_2:th.13">ARYTM_2:13</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">x</font> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c5">x1</font></span>)</span> <a href="arytm_2.html#K8" title="ARYTM_2:func.8">*'</a> <font color="Maroon" title="c4">z</font>
<b>by </b><i><a class="ref" href="arytm_2.html#T13" title="ARYTM_2:th.13">ARYTM_2:13</a></i>
<br/>.= 
<font color="Maroon" title="c4">z</font>
<b>by </b><i><a class="txt" href="arytm_1.html#E4:2"><i><font color="Green" title="E4">A2</font></i></a>, <a class="ref" href="arytm_2.html#T16" title="ARYTM_2:th.16">ARYTM_2:16</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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