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<b>let </b><font color="Maroon">A</font> be  <a href="orders_2.html#V3" target="_self">transitive</a>  <a href="orders_2.html#L1" target="_self">RelStr</a> ;<br/><b>let </b><font color="Maroon">a1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font>, <font color="Maroon">a2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font>, <font color="Maroon">a3</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">A</font>;<br/>



<b>assume </b><a NAME="E1:15"/><i><font color="Green">E18</font></i>: 
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a2</font>,<font color="Maroon">a3</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_2.html#D9" target="_self">ORDERS_2:def 9</a><br/>

<a NAME="E2:15"/><b>then </b>
( <font color="Maroon">a1</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> &amp; <font color="Maroon">a2</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> &amp; <font color="Maroon">a3</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> &amp; the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font> <a href="relat_2.html#R8">is_transitive_in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> )
 
<b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>hence </b><a NAME="E3:15"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">a1</font>,<font color="Maroon">a3</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> the <a href="orders_2.html#U1" target="_self">InternalRel</a> of <font color="Maroon">A</font>
 <b>by </b><i>, <a class="ref" href="relat_2.html#D8">RELAT_2:def 8</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_2.html#D9" target="_self">ORDERS_2:def 9</a><br/>


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