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<b>let </b><font color="Maroon" title="c1">O</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/>

<b>set </b><font color="Maroon" title="c2">RO</font> = the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">O</font>;<br/>
<b>set </b><font color="Maroon" title="c3">CO</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">O</font>;<br/>
<b>assume </b><a NAME="E1:64"/>
<font color="Maroon" title="c1">O</font> is <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>
 ;<br/>

<a NAME="E2:64"/><b>then </b>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">O</font> <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">O</font>
 
<b>by </b><i><a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></i>;<br/>
<a NAME="E3:64"/><b>then </b>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">O</font> is <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a>
 
<b>by </b><i><a class="ref" href="oposet_1.html#T13" target="_self" title="OPOSET_1:th.13">Th13</a></i>;<br/>
<b>hence </b><a NAME="E4:64"/>
<font color="Maroon" title="c1">O</font> is <a href="oposet_1.html#V9" title="OPOSET_1:attr.9">SubTransitive</a>
 <b>by </b><i><a class="ref" href="oposet_1.html#D19" target="_self" title="OPOSET_1:def.19">Def19</a></i>;<br/>


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