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<b>let </b><font color="Maroon">p</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">m</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> ;<br/>



<b>assume </b><a NAME="E1:3"/>
<font color="Maroon">p</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/>

<a NAME="E2:3"/><b>then </b><i><font color="Green">E38</font></i>: 
0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> <a href="xcmplx_0.html#K5">"</a> 
 
<b>by </b><i><a class="ref" href="xreal_1.html#T124">XREAL_1:124</a></i>;<br/>
<b>consider </b><font color="Maroon">k1</font> being    <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a> <b> such that </b><br/><a NAME="E4:3"/><i><font color="Green">E39</font></i>: 
<font color="Maroon">p</font> <a href="xcmplx_0.html#K5">"</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">k1</font>
 <b>by </b><i><a class="ref" href="seq_4.html#T10">SEQ_4:10</a></i>;<br/>
<b>take </b><font color="Maroon">i</font> = <font color="Maroon">k1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font>;<br/>

<a NAME="E5:3"/>
<font color="Maroon">k1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">k1</font> <a href="nat_1.html#K1">+</a> <font color="Maroon">m</font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E6:3"/><b>then </b>
<font color="Maroon">p</font> <a href="xcmplx_0.html#K5">"</a>  <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font>
 
<b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E7:3"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="xcmplx_0.html#K5">"</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/>
<a NAME="E8:3"/><b>then </b>
1 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="xcmplx_0.html#K5">"</a> </span>)</span>
 
<b>by </b><i>, <a class="ref" href="xreal_1.html#T78">XREAL_1:78</a></i>;<br/>
<b>hence </b><a NAME="E9:3"/>
( 1 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p</font> &amp; <font color="Maroon">m</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">i</font> )
 <b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a>, <a class="ref" href="xcmplx_1.html#T218">XCMPLX_1:218</a></i>;<br/>


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