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<b>let </b><font color="Maroon" title="c1">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">R</font> is <a href="orders_1.html#V2" title="ORDERS_1:attr.2">being_partial-order</a> implies <font color="Maroon" title="c1">R</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a>  is <a href="orders_1.html#V2" title="ORDERS_1:attr.2">being_partial-order</a> )</span><br/>

<b>assume </b><a NAME="E1:22"/>
( <font color="Maroon" title="c1">R</font> is <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a> &amp; <font color="Maroon" title="c1">R</font> is <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a> &amp; <font color="Maroon" title="c1">R</font> is <a href="relat_2.html#V4" title="RELAT_2:attr.4">antisymmetric</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_1.html#D4" target="_self" title="ORDERS_1:def.4">ORDERS_1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">R</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a>  is <a href="orders_1.html#V2" title="ORDERS_1:attr.2">being_partial-order</a></span><br/>

<b>hence </b><a NAME="E2:22"/>
( <font color="Maroon" title="c1">R</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a>  is <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a> &amp; <font color="Maroon" title="c1">R</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a>  is <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a> &amp; <font color="Maroon" title="c1">R</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a>  is <a href="relat_2.html#V4" title="RELAT_2:attr.4">antisymmetric</a> )
 <b>by </b><i><a class="ref" href="relat_2.html#T27" title="RELAT_2:th.27">RELAT_2:27</a>, <a class="ref" href="relat_2.html#T40" title="RELAT_2:th.40">RELAT_2:40</a>, <a class="ref" href="relat_2.html#T42" title="RELAT_2:th.42">RELAT_2:42</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_1.html#D4" target="_self" title="ORDERS_1:def.4">ORDERS_1:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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