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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font>, <font color="Maroon" title="c4">r</font> be   <a href="armstrng.html#NM3" title="ARMSTRNG:NM.3">Dependency</a> of <font color="Maroon" title="c1">X</font>;<br/>



<b>assume </b><a NAME="E1:38"/>
( <font color="Maroon" title="c2">p</font> <a href="armstrng.html#NR6" title="ARMSTRNG:NR.6">&lt;=</a> <font color="Maroon" title="c3">q</font> &amp; <font color="Maroon" title="c3">q</font> <a href="armstrng.html#NR6" title="ARMSTRNG:NR.6">&lt;=</a> <font color="Maroon" title="c4">r</font> )
 ;<br/>

<a NAME="E2:38"/><b>then </b>
( <font color="Maroon" title="c3">q</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">p</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  &amp; <font color="Maroon" title="c2">p</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">q</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  &amp; <font color="Maroon" title="c4">r</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">q</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  &amp; <font color="Maroon" title="c3">q</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">r</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  )
 
<b>by </b><i><a class="ref" href="armstrng.html#D10" target="_self" title="ARMSTRNG:def.10">Def10</a></i>;<br/>
<a NAME="E3:38"/><b>then </b>
( <font color="Maroon" title="c4">r</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">p</font> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  &amp; <font color="Maroon" title="c2">p</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c4">r</font> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<b>hence </b><a NAME="E4:38"/>
<font color="Maroon" title="c2">p</font> <a href="armstrng.html#NR6" title="ARMSTRNG:NR.6">&lt;=</a> <font color="Maroon" title="c4">r</font>
 <b>by </b><i><a class="ref" href="armstrng.html#D10" target="_self" title="ARMSTRNG:def.10">Def10</a></i>;<br/>


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