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

<a NAME="E1:101"/>
<font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K5" title="MONOID_0:func.5">&lt;NAT,+,0&gt;</a> ) <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K4" title="MONOID_0:func.4">&lt;NAT,+&gt;</a> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#T18" target="_self" onmouseover="rs('monoid_0/T18')" onmouseout="rh()">Th18</a></span>;<br/>
<a NAME="E2:101"/><span class="kw">then </span>
 <a href="monoid_0.html#K5" title="MONOID_0:func.5">&lt;NAT,+,0&gt;</a>  is    <a href="monoid_0.html#M5" title="MONOID_0:mode.5">SubStr</a> of  <a href="monoid_0.html#K4" title="MONOID_0:func.4">&lt;NAT,+&gt;</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#D23" target="_self" onmouseover="rs('monoid_0/D23')" onmouseout="rh()">Def23</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:101"/>
 for <font color="Olive" title="b1">n1</font>, <font color="Olive" title="b2">n2</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <br/>  for <font color="Olive" title="b3">m1</font>, <font color="Olive" title="b4">m2</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="monoid_0.html#K5" title="MONOID_0:func.5">&lt;NAT,+,0&gt;</a>  st <font color="Olive" title="b1">n1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">m1</font> &amp; <font color="Olive" title="b2">n2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">m2</font> holds <br/><font color="Olive" title="b3">m1</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b4">m2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">n1</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">n2</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#T39" target="_self" onmouseover="rs('monoid_0/T39')" onmouseout="rh()">Th39</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
