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<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:5_1_2"/><i><font color="Green">E3</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="lattice7.html#M1" target="_self">Chain</a> of  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> st <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:5_1_2"/><i><font color="Green">E4</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="lattice7.html#M1" target="_self">Chain</a> of  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> holds  <a href="card_1.html#K4">card</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E3:5_1_2"/><i><font color="Green">E5</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="lattice7.html#M1" target="_self">Chain</a> of  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> st <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Olive">b<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:5_1_2"/><i><font color="Green">E6</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being   <a href="lattice7.html#M1" target="_self">Chain</a> of  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> holds  <a href="card_1.html#K4">card</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>5</sub></font> being    <a href="lattice7.html#M1" target="_self">Chain</a> of  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E6:5_1_2"/><i><font color="Green">E7</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>5</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="lattice7.html#M1" target="_self">Chain</a> of  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> holds  <a href="card_1.html#K4">card</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> ) )
 <b>by </b><i><a class="txt" href="lattice7.html#E1:5_1_2"><i><font color="Green">E3</font></i></a>, <a class="txt" href="lattice7.html#E2:5_1_2"><i><font color="Green">E4</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="lattice7.html#M1" target="_self">Chain</a> of  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E8:5_1_2"/><i><font color="Green">E8</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <font color="Maroon">c<sub>6</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being   <a href="lattice7.html#M1" target="_self">Chain</a> of  <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> holds  <a href="card_1.html#K4">card</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font> ) )
 <b>by </b><i><a class="txt" href="lattice7.html#E3:5_1_2"><i><font color="Green">E5</font></i></a>, <a class="txt" href="lattice7.html#E4:5_1_2"><i><font color="Green">E6</font></i></a></i>;<br/>
<a NAME="E9:5_1_2"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="lattice7.html#E6:5_1_2"><i><font color="Green">E7</font></i></a>, <a class="txt" href="lattice7.html#E8:5_1_2"><i><font color="Green">E8</font></i></a></i>;<br/>
<a NAME="E10:5_1_2"/>
<font color="Maroon">c<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="lattice7.html#E6:5_1_2"><i><font color="Green">E7</font></i></a>, <a class="txt" href="lattice7.html#E8:5_1_2"><i><font color="Green">E8</font></i></a></i>;<br/>
<b>hence </b><a NAME="E11:5_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="txt" href="lattice7.html#E9:5_1_2"><i><font color="Green">E9</font></i></a>, <a class="ref" href="xxreal_0.html#T1">XXREAL_0:1</a></i>;<br/>


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