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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a> ,   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a> ) <b>-&gt; </b>   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>  =  <a href="nat_lat.html#K7" title="NAT_LAT:func.7">@</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="nat_lat.html#K8" title="NAT_LAT:func.8">@</a> $1</span>)</span> <a href="nat_d.html#K6" title="NAT_D:func.6">lcm</a> <span class="p2">(<span class="default"><a href="nat_lat.html#K8" title="NAT_LAT:func.8">@</a> $2</span>)</span></span>)</span>;<br/>
<b>consider </b><font color="Maroon" title="c1">f</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of  <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a> <b> such that </b><br/><a NAME="E2:27_2_1"/><i><font color="Green" title="E10">A4</font></i>: 
for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a>  holds  <font color="Maroon" title="c1">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">m</font>,<font color="Olive" title="b2">n</font>)
 <b>from </b><i><a class="ref" href="binop_1.html#S4" title="BINOP_1:sch.4">BINOP_1:sch 4</a>();<br/></i>
<b>take </b>
<font color="Maroon" title="c1">f</font>
;<br/>

<b>let </b><font color="Maroon" title="c2">m</font>, <font color="Maroon" title="c3">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="nat_lat.html#K6" title="NAT_LAT:func.6">NATPLUS</a> ;<br/>

<a NAME="E3:27_2_1"/><i><font color="Green" title="E11">A5</font></i>: 
<font color="Maroon" title="c2">m</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="nat_lat.html#D9" target="_self" title="NAT_LAT:def.9">Def9</a></i>;<br/>
<a NAME="E4:27_2_1"/><i><font color="Green" title="E12">A6</font></i>: 
<font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="ref" href="nat_lat.html#D9" target="_self" title="NAT_LAT:def.9">Def9</a></i>;<br/>
<a NAME="E5:27_2_1"/><i><font color="Green" title="E13">A7</font></i>: 
 <a href="nat_lat.html#K8" title="NAT_LAT:func.8">@</a> <font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">n</font>
 
;<br/>
<a NAME="E6:27_2_1"/>
 <a href="nat_lat.html#K8" title="NAT_LAT:func.8">@</a> <font color="Maroon" title="c2">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font>
 
;<br/>
<a NAME="E7:27_2_1"/><b>then </b><i><font color="Green" title="E14">A8</font></i>: 
<font color="Maroon" title="c1">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="nat_lat.html#K7" title="NAT_LAT:func.7">@</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">lcm</a> <font color="Maroon" title="c3">n</font></span>)</span>
 
<b>by </b><i><a class="txt" href="nat_lat.html#E2:27_2_1"><i><font color="Green" title="E10">A4</font></i></a>, <a class="txt" href="nat_lat.html#E5:27_2_1"><i><font color="Green" title="E13">A7</font></i></a></i>;<br/>
<a NAME="E8:27_2_1"/>
<font color="Maroon" title="c2">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">lcm</a> <font color="Maroon" title="c3">n</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<b>by </b><i><a class="txt" href="nat_lat.html#E3:27_2_1"><i><font color="Green" title="E11">A5</font></i></a>, <a class="txt" href="nat_lat.html#E4:27_2_1"><i><font color="Green" title="E12">A6</font></i></a>, <a class="ref" href="newton.html#T73" title="NEWTON:th.73">NEWTON:73</a></i>;<br/>
<b>hence </b><a NAME="E9:27_2_1"/>
<font color="Maroon" title="c1">f</font> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> <font color="Maroon" title="c2">m</font>,<font color="Maroon" title="c3">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">m</font> <a href="nat_d.html#K6" title="NAT_D:func.6">lcm</a> <font color="Maroon" title="c3">n</font>
 <b>by </b><i><a class="txt" href="nat_lat.html#E7:27_2_1"><i><font color="Green" title="E14">A8</font></i></a>, <a class="ref" href="nat_lat.html#D10" target="_self" title="NAT_LAT:def.10">Def10</a></i>;<br/>


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