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<b>consider </b><font color="Maroon" title="c2">R</font> being   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a><b> such that </b><br/><a NAME="E2:10_1_1"/><i><font color="Green" title="E6">A1</font></i>: 
<font color="Maroon" title="c2">R</font> is <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>
 <b>and </b><br/><a NAME="E3:10_1_1"/><i><font color="Green" title="E7">A2</font></i>: 
 <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 <b>by </b><i><a class="ref" href="wellset1.html#T9" title="WELLSET1:th.9">WELLSET1:9</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c3">R</font> = <font color="Maroon" title="c2">R</font> as   <a href="relset_1.html#NM3" title="RELSET_1:NM.3">Relation</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="polynom1.html#E3:10_1_1"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="polynom1.html#T4" target="_self" title="POLYNOM1:th.4">Th4</a></i>;<br/>
<a NAME="E5:10_1_1"/><i><font color="Green" title="E8">A3</font></i>: 
( <font color="Maroon" title="c3">R</font> is <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a> &amp; <font color="Maroon" title="c3">R</font> is <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a> &amp; <font color="Maroon" title="c3">R</font> is <a href="relat_2.html#V4" title="RELAT_2:attr.4">antisymmetric</a> &amp; <font color="Maroon" title="c3">R</font> is <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a> &amp; <font color="Maroon" title="c3">R</font> is <a href="wellord1.html#V1" title="WELLORD1:attr.1">well_founded</a> )
 
<b>by </b><i><a class="txt" href="polynom1.html#E2:10_1_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="wellord1.html#D4" title="WELLORD1:def.4">WELLORD1:def 4</a></i>;<br/>
<a NAME="E6:10_1_1"/><b>then </b>
<font color="Maroon" title="c3">R</font> <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="polynom1.html#E3:10_1_1"><i><font color="Green" title="E7">A2</font></i></a>, <a class="ref" href="relat_2.html#D9" title="RELAT_2:def.9">RELAT_2:def 9</a></i>;<br/>
<a NAME="E7:10_1_1"/><b>then </b>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="ref" href="orders_1.html#T98" title="ORDERS_1:th.98">ORDERS_1:98</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">R</font> = <font color="Maroon" title="c3">R</font> as   <a href="orders_1.html#NM2" title="ORDERS_1:NM.2">Order</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="txt" href="polynom1.html#E2:10_1_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="ref" href="partfun1.html#D4" title="PARTFUN1:def.4">PARTFUN1:def 4</a>, <a class="ref" href="wellord1.html#D4" title="WELLORD1:def.4">WELLORD1:def 4</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">R</font>
;<br/>

<b>thus </b><a NAME="E9:10_1_1"/>
( <font color="Maroon" title="c4">R</font> is <a href="orders_1.html#V3" title="ORDERS_1:attr.3">being_linear-order</a> &amp; <font color="Maroon" title="c4">R</font> is <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> )
 <b>by </b><i><a class="txt" href="polynom1.html#E2:10_1_1"><i><font color="Green" title="E6">A1</font></i></a>, <a class="txt" href="polynom1.html#E5:10_1_1"><i><font color="Green" title="E8">A3</font></i></a>, <a class="ref" href="orders_1.html#D5" title="ORDERS_1:def.5">ORDERS_1:def 5</a></i>;<br/>


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