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<span class="kw">set </span><font color="Maroon" title="c1">R</font> =  the   <a href="orders_1.html#NM2" title="ORDERS_1:NM.2">Order</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c2">L</font> =  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>, the   <a href="orders_1.html#NM2" title="ORDERS_1:NM.2">Order</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> #); <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="c2">L</font> is  <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="orders_2.html#V2" title="ORDERS_2:attr.2">total</a>  &amp; <font color="Maroon" title="c2">L</font> is 1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>  )</span><br/>

<a NAME="E1:4_1_1"/><span class="lab"><font color="Green" title="E5">A1</font></span>: 
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a>  the   <a href="orders_1.html#NM2" title="ORDERS_1:NM.2">Order</a> of <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="orders_1.html#T12" title="ORDERS_1:th.12">ORDERS_1:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:4_1_1"/>
 the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L</font> <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="relat_2.html#D9" title="RELAT_2:def.9">RELAT_2:def 9</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="orders_2.html#D2" target="_self" title="ORDERS_2:def.2">ORDERS_2:def 2</a> <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="c2">L</font> is  <a href="orders_2.html#V4" title="ORDERS_2:attr.4">transitive</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="orders_2.html#V2" title="ORDERS_2:attr.2">total</a>  &amp; <font color="Maroon" title="c2">L</font> is 1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E3:4_1_1"/>
 the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L</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="c2">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:4_1_1"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="relat_2.html#D16" title="RELAT_2:def.16">RELAT_2:def 16</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="orders_2.html#D3" target="_self" 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"> ( <font color="Maroon" title="c2">L</font> is  <a href="orders_2.html#V5" title="ORDERS_2:attr.5">antisymmetric</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="orders_2.html#V2" title="ORDERS_2:attr.2">total</a>  &amp; <font color="Maroon" title="c2">L</font> is 1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E4:4_1_1"/>
 the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L</font> <a href="relat_2.html#R4" title="RELAT_2:pred.4">is_antisymmetric_in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:4_1_1"><span class="lab"><font color="Green" title="E5">A1</font></span></a>, <a class="ref" href="relat_2.html#D12" title="RELAT_2:def.12">RELAT_2:def 12</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="orders_2.html#D4" target="_self" title="ORDERS_2:def.4">ORDERS_2:def 4</a> <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="c2">L</font> is  <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a>  &amp; <font color="Maroon" title="c2">L</font> is  <a href="orders_2.html#V2" title="ORDERS_2:attr.2">total</a>  &amp; <font color="Maroon" title="c2">L</font> is 1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E5:4_1_1"/>
<font color="Maroon" title="c2">L</font> is  <a href="orders_2.html#V1" title="ORDERS_2:attr.1">strict</a> 
 ; <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="c2">L</font> is  <a href="orders_2.html#V2" title="ORDERS_2:attr.2">total</a>  &amp; <font color="Maroon" title="c2">L</font> is 1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E6:4_1_1"/>
 the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">L</font> is  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="orders_2.html#D1" target="_self" title="ORDERS_2:def.1">ORDERS_2:def 1</a> <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="c2">L</font> is 1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a> </span><br/>

<span class="kw">thus </span><a NAME="E7:4_1_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">L</font> is 1 <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="struct_0.html#D19" title="STRUCT_0:def.19">STRUCT_0:def 19</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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