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<span class="kw">thus </span><a NAME="E1:33_1_1"/>
( <font color="Maroon" title="c1">O</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  implies  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>  <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">O</font> )
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  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>  <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">O</font> implies <font color="Maroon" title="c1">O</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  )</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="33_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:33_1_1_1"/>
 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>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="orders_2.html#D3" title="ORDERS_2:def.3">ORDERS_2:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  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>  <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">O</font></span><br/>

<span class="kw">hence </span><a NAME="E2:33_1_1_1"/>
 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>  <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">O</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partit_2.html#T27" title="PARTIT_2:th.27">PARTIT_2:27</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:33_1_1"/>
 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>  <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">O</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">O</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a> </span><br/>

<span class="kw">hence </span><a NAME="E3:33_1_1"/>
 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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="partit_2.html#T26" title="PARTIT_2:th.26">PARTIT_2:26</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="orders_2.html#D3" title="ORDERS_2:def.3">ORDERS_2:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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