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<b>let </b><font color="Maroon">b</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">c</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>



<a NAME="E1:218"/>
( ( for <font color="Olive">a</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st <font color="Olive">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 holds <br/><font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font> ) implies <font color="Maroon">b</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="218_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:218_1"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">a</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st <font color="Olive">a</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 holds <br/><font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="218_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">d</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><a NAME="E1:218_1_1"/><i><font color="Green">E33</font></i>: 
<font color="Maroon">d</font> <a href="xcmplx_0.html#K5">"</a>  <a href="hidden.html#R1">=</a> 1 <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">d</font>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T217">XCMPLX_1:217</a></i>;<br/><b>assume </b><a NAME="E2:218_1_1"/><i><font color="Green">E39</font></i>: 
( 0 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">d</font> &amp; <font color="Maroon">d</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> 1 )
 ;<br/><a NAME="E3:218_1_1"/><b>then </b>
<font color="Maroon">d</font> <a href="xcmplx_0.html#K5">"</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 1 <a href="xcmplx_0.html#K5">"</a> 
 <b>by </b><i/>;<br/><a NAME="E4:218_1_1"/><b>then </b>
<font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <span class="p1">(<span class="default"><font color="Maroon">d</font> <a href="xcmplx_0.html#K5">"</a> </span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i/>;<br/><a NAME="E5:218_1_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">b</font> <a href="xcmplx_0.html#K3">*</a> <font color="Maroon">d</font></span>)</span> <a href="xcmplx_0.html#K7">/</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i><a class="ref" href="xcmplx_1.html#T78">XCMPLX_1:78</a>, </i>;<br/><b>hence </b><a NAME="E6:218_1_1"/>
<font color="Maroon">b</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font> <a href="xcmplx_0.html#K7">/</a> <font color="Maroon">d</font>
 <b>by </b><i>, </i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:218_1"/>
<font color="Maroon">b</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font>
 <b>by </b><i/>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:218"/>
( ( for <font color="Olive">a</font> being <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a>   st 1 <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Olive">a</font> holds <br/><font color="Maroon">b</font> <a href="xcmplx_0.html#K7">/</a> <font color="Olive">a</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font> ) implies <font color="Maroon">b</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c</font> )
 ;<br/>


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