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<span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:110"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c1">R</font> is  <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a> 
 <span class="kw">and </span><br/><a NAME="E2:110"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
<font color="Maroon" title="c1">R</font> is  <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a> 
 <span class="kw">and </span><br/><a NAME="E3:110"/><span class="lab"><font color="Green" title="E14">A3</font></span>: 
<font color="Maroon" title="c1">R</font> is  <a href="relat_2.html#V4" title="RELAT_2:attr.4">antisymmetric</a> 
 ; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">thus </span><a NAME="E4:110"/>
( <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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:110"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E2:110"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E3:110"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <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></span>; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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