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<b>let </b><font color="Maroon" title="c1">f</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>



<b>assume </b><a NAME="E1:17"/><i><font color="Green" title="E12">A1</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c1">f</font>
 ;<br/>

<a NAME="E2:17"/><i><font color="Green" title="E13">A2</font></i>: 
 <a href="jordan1h.html#K1" title="JORDAN1H:func.1">RealOrd</a>  <a href="orders_1.html#R3" title="ORDERS_1:pred.3">linearly_orders</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="jordan1h.html#T11" target="_self" title="JORDAN1H:th.11">Th11</a>, <a class="ref" href="orders_1.html#T134" title="ORDERS_1:th.134">ORDERS_1:134</a></i>;<br/>
<a NAME="E3:17"/><b>then </b><i><font color="Green" title="E14">A3</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><a href="triang_1.html#K2" title="TRIANG_1:func.2">SgmX</a> <a href="jordan1h.html#K1" title="JORDAN1H:func.1">RealOrd</a> ,<font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c1">f</font>
 
<b>by </b><i><a class="txt" href="jordan1h.html#E1:17"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="triang_1.html#D2" title="TRIANG_1:def.2">TRIANG_1:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">F</font> =  <a href="triang_1.html#K2" title="TRIANG_1:func.2">SgmX</a> <a href="jordan1h.html#K1" title="JORDAN1H:func.1">RealOrd</a> ,<font color="Maroon" title="c2">A</font> as  <a href="goboard1.html#V1" title="GOBOARD1:attr.1">increasing</a>  <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a>  <b>by </b><i><a class="ref" href="jordan1h.html#T12" target="_self" title="JORDAN1H:th.12">Th12</a></i>;<br/>
<a NAME="E5:17"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">F</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c1">f</font></span>)</span>
 
<b>by </b><i><a class="txt" href="jordan1h.html#E1:17"><i><font color="Green" title="E12">A1</font></i></a>, <a class="txt" href="jordan1h.html#E2:17"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="triang_1.html#T9" title="TRIANG_1:th.9">TRIANG_1:9</a></i>;<br/>
<b>hence </b><a NAME="E6:17"/>
 <a href="triang_1.html#K2" title="TRIANG_1:func.2">SgmX</a> <a href="jordan1h.html#K1" title="JORDAN1H:func.1">RealOrd</a> ,<font color="Maroon" title="c2">A</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="goboard2.html#K2" title="GOBOARD2:func.2">Incr</a> <font color="Maroon" title="c1">f</font>
 <b>by </b><i><a class="txt" href="jordan1h.html#E3:17"><i><font color="Green" title="E14">A3</font></i></a>, <a class="ref" href="goboard2.html#D2" title="GOBOARD2:def.2">GOBOARD2:def 2</a></i>;<br/>


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