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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"> for <font color="Olive" title="b1">Y</font>, <font color="Olive" title="b2">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#R2" title="ORDERS_1:pred.2">partially_orders</a> <font color="Olive" title="b1">Y</font> &amp; <font color="Olive" title="b2">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Olive" title="b1">Y</font> holds <br/><font color="Maroon" title="c1">R</font> <a href="orders_1.html#R2" title="ORDERS_1:pred.2">partially_orders</a> <font color="Olive" title="b2">X</font></span><br/><b>let </b><font color="Maroon" title="c2">Y</font>, <font color="Maroon" title="c3">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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="orders_1.html#R2" title="ORDERS_1:pred.2">partially_orders</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> implies <font color="Maroon" title="c1">R</font> <a href="orders_1.html#R2" title="ORDERS_1:pred.2">partially_orders</a> <font color="Maroon" title="c3">X</font> )</span><br/>





<b>assume </b><a NAME="E1:49"/>
( <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">Y</font> &amp; <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">Y</font> &amp; <font color="Maroon" title="c1">R</font> <a href="relat_2.html#R4" title="RELAT_2:pred.4">is_antisymmetric_in</a> <font color="Maroon" title="c2">Y</font> &amp; <font color="Maroon" title="c3">X</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">Y</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_1.html#D7" target="_self" title="ORDERS_1:def.7">ORDERS_1:def 7</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="orders_1.html#R2" title="ORDERS_1:pred.2">partially_orders</a> <font color="Maroon" title="c3">X</font></span><br/>

<b>hence </b><a NAME="E2:49"/>
( <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="c3">X</font> &amp; <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="c3">X</font> &amp; <font color="Maroon" title="c1">R</font> <a href="relat_2.html#R4" title="RELAT_2:pred.4">is_antisymmetric_in</a> <font color="Maroon" title="c3">X</font> )
 <b>by </b><i><a class="ref" href="orders_1.html#T93" target="_self" title="ORDERS_1:th.93">Th93</a>, <a class="ref" href="orders_1.html#T94" target="_self" title="ORDERS_1:th.94">Th94</a>, <a class="ref" href="orders_1.html#T95" target="_self" title="ORDERS_1:th.95">Th95</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_1.html#D7" target="_self" title="ORDERS_1:def.7">ORDERS_1:def 7</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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