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<b>let </b><font color="Maroon">N</font> be  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V2">unital</a>  <a href="monoid_0.html#M2" target="_self">SubStr</a> of  <a href="monoid_0.html#K7" target="_self">&lt;REAL,*&gt;</a> ;<br/>

<b>set </b><font color="Maroon">e</font> =  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">N</font>);<br/>
<a NAME="E1:118"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">N</font>) <a href="tarski.html#R1">c=</a> <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K7" target="_self">&lt;REAL,*&gt;</a> )
 
<b>by </b><i/>;<br/>
<b>then reconsider </b><font color="Maroon">x</font> =  <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">N</font>) as   <a href="real_1.html#NM1">Real</a> <b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<a NAME="E3:118"/>
 <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">N</font>) <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">N</font>)
 
<b>by </b><i/>;<br/>
<b>then </b> <a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">N</font>) = 
<span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">N</font>)</span>)</span> <a href="group_1.html#K10">*</a> <span class="p1">(<span class="default"><a href="binop_1.html#K3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">N</font>)</span>)</span>
<b>by </b><i><a class="ref" href="binop_1.html#T11">BINOP_1:11</a></i>
<br/>.= 
<font color="Maroon">x</font> <a href="binop_2.html#K11">*</a> <font color="Maroon">x</font>
<b>by </b><i><a class="ref" href="monoid_0.html#T4" target="_self">Th4</a></i>
;<br/>
<a NAME="E5:118"/><b>then </b>
<font color="Maroon">x</font> <a href="binop_2.html#K11">*</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">x</font> <a href="binop_2.html#K11">*</a> <font color="Maroon">x</font>
 
;<br/>
<b>hence </b><a NAME="E6:118"/>
(  <a href="binop_1.html#K3">the_unity_wrt</a> the <a href="group_1.html#U1">mult</a> of <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> 0 or  <a href="binop_1.html#K3">the_unity_wrt</a> the <a href="group_1.html#U1">mult</a> of <font color="Maroon">N</font> <a href="hidden.html#R1">=</a> 1 )
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T5">XCMPLX_1:5</a></i>;<br/>


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