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<a NAME="E1:114"/>
( <font color="Maroon">H<sub>1</sub></font>( <a href="monoid_0.html#K5" target="_self">&lt;NAT,+&gt;</a> ) <a href="hidden.html#R1">=</a>  <a href="numbers.html#K5">NAT</a>  &amp; <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K3" target="_self">&lt;REAL,+&gt;</a> ) <a href="funct_2.html#R1">=</a>  <a href="binop_2.html#K33">addreal</a>  &amp; <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K4" target="_self">INT.Group</a> ) <a href="funct_2.html#R1">=</a>  <a href="binop_2.html#K44">addint</a>  &amp; <font color="Maroon">H<sub>2</sub></font>( <a href="monoid_0.html#K5" target="_self">&lt;NAT,+&gt;</a> ) <a href="funct_2.html#R1">=</a>  <a href="binop_2.html#K47">addnat</a>  )
 
<b>by </b><i><a class="ref" href="monoid_0.html#D16" target="_self">Def16</a>, <a class="ref" href="gr_cy_1.html#D4">GR_CY_1:def 4</a></i>;<br/>
<b>hence </b><a NAME="E2:114"/>
(  <a href="binop_2.html#K47">addnat</a>  <a href="hidden.html#R1">=</a> <a href="binop_2.html#K33">addreal</a>  <a href="realset1.html#K1">||</a> <a href="numbers.html#K5">NAT</a>  &amp;  <a href="binop_2.html#K47">addnat</a>  <a href="hidden.html#R1">=</a> <a href="binop_2.html#K44">addint</a>  <a href="realset1.html#K1">||</a> <a href="numbers.html#K5">NAT</a>  )
 <b>by </b><i><a class="ref" href="monoid_0.html#D5" target="_self">Def5</a></i>;<br/>


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