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<b>let </b><font color="Maroon">a</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="algstr_1.html#K6" target="_self">multEX_0</a> , <font color="Maroon">b</font> be   <a href="struct_0.html#NM1">Element</a> of <a href="algstr_1.html#K6" target="_self">multEX_0</a> ;<br/>

<b>assume </b><a NAME="E1:51"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <a href="algstr_1.html#K6" target="_self">multEX_0</a> 
 ;<br/>

<b>reconsider </b><font color="Maroon">p</font> = <font color="Maroon">a</font>, <font color="Maroon">q</font> = <font color="Maroon">b</font> as   <a href="real_1.html#NM1">Real</a> ;<br/>
<b>consider </b><font color="Maroon">r</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E4:51"/><i><font color="Green">E25</font></i>: 
<font color="Maroon">p</font> <a href="binop_2.html#K11">*</a> <font color="Maroon">r</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font>
 <b>by </b><i><a class="txt" href="algstr_1.html#E24"><i><font color="Green">Lemma44</font></i></a>, <a class="ref" href="algstr_1.html#D9" target="_self">Def9</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x</font> = <font color="Maroon">r</font> as   <a href="struct_0.html#NM1">Element</a> of <a href="algstr_1.html#K6" target="_self">multEX_0</a>  ;<br/>
<a NAME="E6:51"/>
<font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 
<b>by </b><i><a class="txt" href="algstr_1.html#E25"><i><font color="Green">Lemma45</font></i></a>, <a class="ref" href="algstr_1.html#D5" target="_self">Def5</a></i>;<br/>
<b>hence </b><a NAME="E7:51"/>
 ex <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <a href="algstr_1.html#K6" target="_self">multEX_0</a>  st <font color="Maroon">a</font> <a href="group_1.html#K1">*</a> <font color="Olive">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">b</font>
 ;<br/>


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