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<span class="kw">consider </span><font color="Maroon" title="c2">R</font> being   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a><span class="kw"> such that </span><br/><a NAME="E2:46_1_1"/><span class="lab"><font color="Green" title="E15">A1</font></span>: 
<font color="Maroon" title="c2">R</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> 
 <span class="kw">and </span><br/><a NAME="E3:46_1_1"/><span class="lab"><font color="Green" title="E16">A2</font></span>: 
 <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>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="wellset1.html#T6" title="WELLSET1:th.6">WELLSET1:6</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">R</font> = <font color="Maroon" title="c2">R</font> as   <a href="relset_1.html#NM2" title="RELSET_1:NM.2">Relation</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46_1_1"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="pre_poly.html#T18" target="_self" title="PRE_POLY:th.18">Th18</a></span>;<br/>
<a NAME="E5:46_1_1"/><span class="lab"><font color="Green" title="E17">A3</font></span>: 
<font color="Maroon" title="c3">R</font> is  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="wellord1.html#D4" title="WELLORD1:def.4">WELLORD1:def 4</a></span>;<br/>
<a NAME="E6:46_1_1"/>
<font color="Maroon" title="c3">R</font> is  <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="wellord1.html#D4" title="WELLORD1:def.4">WELLORD1:def 4</a></span>;<br/>
<a NAME="E7:46_1_1"/><span class="kw">then </span>
<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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:46_1_1"><span class="lab"><font color="Green" title="E16">A2</font></span></a>, <a class="ref" href="relat_2.html#D9" title="RELAT_2:def.9">RELAT_2:def 9</a></span>;<br/>
<a NAME="E8:46_1_1"/><span class="kw">then </span>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="orders_1.html#T13" title="ORDERS_1:th.13">ORDERS_1:13</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><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> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="ref" href="partfun1.html#D2" title="PARTFUN1:def.2">PARTFUN1:def 2</a>, <a class="ref" href="wellord1.html#D4" title="WELLORD1:def.4">WELLORD1:def 4</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c4">R</font>
; <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="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>  )</span><br/>

<span class="kw">thus </span><a NAME="E10:46_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>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:46_1_1"><span class="lab"><font color="Green" title="E15">A1</font></span></a>, <a class="txt" href="#E5:46_1_1"><span class="lab"><font color="Green" title="E17">A3</font></span></a>, <a class="ref" href="orders_1.html#D5" title="ORDERS_1:def.5">ORDERS_1:def 5</a></span>; <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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