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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="finset_1.html#V1">finite</a> <a href="subset_1.html#NM2">Subset</a> of <a href="numbers.html#K1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:18"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<a NAME="E2:18"/><i><font color="Green">E13</font></i>: 
 <a href="jordan1h.html#K1" target="_self">RealOrd</a>  <a href="orders_1.html#R3">linearly_orders</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="jordan1h.html#T11" target="_self">Th11</a>, <a class="ref" href="orders_1.html#T134">ORDERS_1:134</a></i>;<br/>
<a NAME="E3:18"/><b>then </b><i><font color="Green">E14</font></i>: 
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2">SgmX</a> <a href="jordan1h.html#K1" target="_self">RealOrd</a> ,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="jordan1h.html#E1:18"><i><font color="Green">E12</font></i></a>, <a class="ref" href="triang_1.html#D2">TRIANG_1:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="triang_1.html#K2">SgmX</a> <a href="jordan1h.html#K1" target="_self">RealOrd</a> ,<font color="Maroon">c<sub>2</sub></font> as  <a href="goboard1.html#V1">increasing</a>  <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K1">REAL</a>  <b>by </b><i><a class="ref" href="jordan1h.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E5:18"/>
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K4">card</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan1h.html#E1:18"><i><font color="Green">E12</font></i></a>, <a class="txt" href="jordan1h.html#E2:18"><i><font color="Green">E13</font></i></a>, <a class="ref" href="triang_1.html#T9">TRIANG_1:9</a></i>;<br/>
<b>hence </b><a NAME="E6:18"/>
 <a href="triang_1.html#K2">SgmX</a> <a href="jordan1h.html#K1" target="_self">RealOrd</a> ,<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="goboard2.html#K2">Incr</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="jordan1h.html#E3:18"><i><font color="Green">E14</font></i></a>, <a class="ref" href="goboard2.html#D2">GOBOARD2:def 2</a></i>;<br/>


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