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<font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K4" title="MONOID_0:func.4">&lt;NAT,+&gt;</a> ) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#D27" target="_self" title="MONOID_0:def.27">Def27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:110"/>
(  <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K33" title="BINOP_2:func.33">addreal</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> &amp;  <a href="binop_2.html#K47" title="BINOP_2:func.47">addnat</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="binop_2.html#K44" title="BINOP_2:func.44">addint</a> <a href="realset1.html#K1" title="REALSET1:func.1">||</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="monoid_0.html#T24" target="_self" title="MONOID_0:th.24">Th26</a>, <a class="ref" href="gr_cy_1.html#D3" title="GR_CY_1:def.3">GR_CY_1:def 3</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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