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<b>let </b><font color="Maroon">i</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">j</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">m</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> , <font color="Maroon">n</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:6"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">n</font>
 <b>and </b><br/><a NAME="E2:6"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">m</font>
 <b>and </b><br/><a NAME="E3:6"/><i><font color="Green">E40</font></i>: 
<font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">n</font>
 ;<br/>

<b>consider </b><font color="Maroon">k</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E5:6"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">m</font> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<b>consider </b><font color="Maroon">l</font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E7:6"/><i><font color="Green">E42</font></i>: 
<font color="Maroon">n</font> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">l</font>
 <b>by </b><i>, <a class="ref" href="nat_1.html#T28">NAT_1:28</a></i>;<br/>
<a NAME="E8:6"/>
<font color="Maroon">i</font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">k</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">n</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">j</font>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:6"/><b>then </b>
<font color="Maroon">j</font> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><font color="Maroon">l</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">j</font> <a href="nat_1.html#K1">+</a> 0
 
<b>by </b><i/>;<br/>
<a NAME="E10:6"/><b>then </b>
<font color="Maroon">l</font> <a href="xcmplx_0.html#K2">+</a> <font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 0
 
;<br/>
<a NAME="E11:6"/><b>then </b>
<font color="Maroon">k</font> <a href="hidden.html#R1">=</a> 0
 
<b>by </b><i><a class="ref" href="nat_1.html#T23">NAT_1:23</a></i>;<br/>
<b>hence </b><a NAME="E12:6"/>
<font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">m</font>
 <b>by </b><i/>;<br/>


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