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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"> for <font color="Olive" title="b1">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Maroon" title="c1">R</font> <a href="orders_1.html#R1" title="ORDERS_1:pred.1">quasi_orders</a> <font color="Olive" title="b1">X</font> holds <br/><font color="Maroon" title="c1">R</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a>  <a href="orders_1.html#R1" title="ORDERS_1:pred.1">quasi_orders</a> <font color="Olive" title="b1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="orders_1.html#R1" title="ORDERS_1:pred.1">quasi_orders</a> <font color="Maroon" title="c2">X</font> implies <font color="Maroon" title="c1">R</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a>  <a href="orders_1.html#R1" title="ORDERS_1:pred.1">quasi_orders</a> <font color="Maroon" title="c2">X</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:155"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
<font color="Maroon" title="c1">R</font> <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a> <font color="Maroon" title="c2">X</font>
 <span class="kw">and </span><br/><a NAME="E2:155"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
<font color="Maroon" title="c1">R</font> <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_in</a> <font color="Maroon" title="c2">X</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="orders_1.html#D6" target="_self" title="ORDERS_1:def.6">ORDERS_1:def 6</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>  <a href="orders_1.html#R1" title="ORDERS_1:pred.1">quasi_orders</a> <font color="Maroon" title="c2">X</font></span><br/>

<span class="kw">thus </span><a NAME="E3:155"/>
( <font color="Maroon" title="c1">R</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a>  <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a> <font color="Maroon" title="c2">X</font> &amp; <font color="Maroon" title="c1">R</font> <a href="relat_1.html#K4" title="RELAT_1:func.4">~</a>  <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_in</a> <font color="Maroon" title="c2">X</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:155"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="txt" href="#E2:155"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="txt" href="orders_1.html#E154"><span class="lab"><font color="Green" title="E28">Lm11</font></span></a>, <a class="txt" href="orders_1.html#E155"><span class="lab"><font color="Green" title="E29">Lm12</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="orders_1.html#D6" target="_self" title="ORDERS_1:def.6">ORDERS_1:def 6</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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