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<b>let </b><font color="Maroon">f</font> be    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="numbers.html#K4">INT</a> ;<br/><b>let </b><font color="Maroon">k</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="2_1"><b>now </b></a><div class="add"><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> ;<br/><b>assume </b><a NAME="E1:2_1"/><i><font color="Green">E44</font></i>: 
( <font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> &amp; <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font> &amp; <font color="Maroon">j</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k</font> )
 ;<br/><a NAME="E2:2_1"/><b>then </b>
<font color="Maroon">k</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">j</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T2">XREAL_1:2</a></i>;<br/><a NAME="E3:2_1"/><b>then </b>
<font color="Maroon">j</font> <a href="hidden.html#R1">=</a> <font color="Maroon">k</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T1">XREAL_1:1</a></i>;<br/><b>hence </b><a NAME="E4:2_1"/>
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">j</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T1">XREAL_1:1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:2"/>
<font color="Maroon">f</font> <a href="sfmastr3.html#R1">is_non_decreasing_on</a> <font color="Maroon">k</font>,<font color="Maroon">k</font>
 <b>by </b><i><a class="ref" href="sfmastr3.html#D4">SFMASTR3:def 4</a></i>;<br/>


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