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

<b>let </b><font color="Maroon" title="c1">N</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="group_1.html#V1" title="GROUP_1:attr.1">unital</a>  <a href="monoid_0.html#M2" title="MONOID_0:mode.2">SubStr</a> of  <a href="monoid_0.html#K6" title="MONOID_0:func.6">&lt;REAL,*&gt;</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )</span><br/>

<b>set </b><font color="Maroon" title="c2">e</font> =  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">N</font>);<br/>
<a NAME="E1:114"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c1">N</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K6" title="MONOID_0:func.6">&lt;REAL,*&gt;</a> )
 
<b>by </b><i><a class="ref" href="monoid_0.html#T25" target="_self" title="MONOID_0:th.25">Th25</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c3">x</font> =  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">N</font>) as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <b>by </b><i><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></i>;<br/>
<a NAME="E3:114"/>
 <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">N</font>) <a href="binop_1.html#R3" title="BINOP_1:pred.3">is_a_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">N</font>)
 
<b>by </b><i><a class="ref" href="monoid_0.html#T4" target="_self" title="MONOID_0:th.4">Th4</a></i>;<br/>
<b>then </b> <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">N</font>) = 
<span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">N</font>)</span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon" title="c1">N</font>)</span>)</span>
<b>by </b><i><a class="ref" href="binop_1.html#T11" title="BINOP_1:th.11">BINOP_1:11</a></i>
<br/>.= 
<font color="Maroon" title="c3">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c3">x</font>
<b>by </b><i><a class="ref" href="monoid_0.html#T58" target="_self" title="MONOID_0:th.58">Th58</a></i>
;<br/>
<a NAME="E5:114"/><b>then </b>
<font color="Maroon" title="c3">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> <a href="binop_2.html#K11" title="BINOP_2:func.11">*</a> <font color="Maroon" title="c3">x</font>
 
;<br/>
<b>hence </b><a NAME="E6:114"/>
(  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="binop_1.html#K3" title="BINOP_1:func.3">the_unity_wrt</a> the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Maroon" title="c1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T5" title="XCMPLX_1:th.5">XCMPLX_1:5</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
