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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="nat_lat.html#M1" target="_self">Element</a> of  <a href="nat_lat.html#K7" target="_self">NATPLUS</a> ,   <a href="nat_lat.html#M1" target="_self">Element</a> of  <a href="nat_lat.html#K7" target="_self">NATPLUS</a> ) <b>-&gt; </b>   <a href="nat_lat.html#M1" target="_self">Element</a> of  <a href="nat_lat.html#K7" target="_self">NATPLUS</a>  =  <a href="nat_lat.html#K8" target="_self">@</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nat_lat.html#K9" target="_self">@</a> <font color="Maroon">a<sub>1</sub></font></span>)</span> <a href="nat_1.html#K8">hcf</a> <span class="p2">(<span class="default"><a href="nat_lat.html#K9" target="_self">@</a> <font color="Maroon">a<sub>2</sub></font></span>)</span></span>)</span>;<br/>
<b>consider </b><font color="Maroon">c<sub>1</sub></font> being   <a href="binop_1.html#NM2">BinOp</a> of  <a href="nat_lat.html#K7" target="_self">NATPLUS</a> <b> such that </b><br/><a NAME="E2:32_1_1"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="nat_lat.html#M1" target="_self">Element</a> of  <a href="nat_lat.html#K7" target="_self">NATPLUS</a>  holds <font color="Maroon">c<sub>1</sub></font> <a href="binop_1.html#K2">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>)
 <b>from </b><i><a class="ref" href="binop_1.html#S4">BINOP_1:sch 4</a>();<br/></i>
<b>take </b>
<font color="Maroon">c<sub>1</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="nat_lat.html#M1" target="_self">Element</a> of  <a href="nat_lat.html#K7" target="_self">NATPLUS</a> ;<br/>

<a NAME="E3:32_1_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="ref" href="nat_lat.html#D9" target="_self">Def9</a></i>;<br/>
<a NAME="E4:32_1_1"/><i><font color="Green">E21</font></i>: 
(  <a href="nat_lat.html#K9" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="nat_lat.html#K9" target="_self">@</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K9" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="nat_lat.html#K9" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font> )
 
;<br/>
<a NAME="E5:32_1_1"/>
(  <a href="nat_lat.html#K9" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="nat_lat.html#K9" target="_self">@</a> <span class="p1">(<span class="default"><a href="nat_lat.html#K9" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="nat_lat.html#K9" target="_self">@</a> <font color="Maroon">c<sub>2</sub></font> )
 
;<br/>
<a NAME="E6:32_1_1"/><b>then </b><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="nat_lat.html#K8" target="_self">@</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K8">hcf</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="nat_lat.html#E2:32_1_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="nat_lat.html#E4:32_1_1"><i><font color="Green">E21</font></i></a></i>;<br/>
<a NAME="E7:32_1_1"/>
<font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K8">hcf</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 
<b>by </b><i><a class="txt" href="nat_lat.html#E3:32_1_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="newton.html#T71">NEWTON:71</a></i>;<br/>
<b>hence </b><a NAME="E8:32_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="nat_1.html#K8">hcf</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="nat_lat.html#E6:32_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="nat_lat.html#D10" target="_self">Def10</a></i>;<br/>


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