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<span class="kw">let </span><font color="Maroon" title="c1">R</font>, <font color="Maroon" title="c2">S</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="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">F</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Maroon" title="c1">R</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>  &amp; <font color="Olive" title="b1">F</font> <a href="wellord1.html#R3" title="WELLORD1:pred.3">is_isomorphism_of</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">S</font> holds <br/><font color="Maroon" title="c2">S</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</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="c1">R</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>  &amp; <font color="Maroon" title="c3">F</font> <a href="wellord1.html#R3" title="WELLORD1:pred.3">is_isomorphism_of</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">S</font> implies <font color="Maroon" title="c2">S</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:54"/>
( <font color="Maroon" title="c1">R</font> is  <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a>  &amp; <font color="Maroon" title="c1">R</font> is  <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a>  &amp; <font color="Maroon" title="c1">R</font> is  <a href="relat_2.html#V4" title="RELAT_2:attr.4">antisymmetric</a>  &amp; <font color="Maroon" title="c1">R</font> is  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>  &amp; <font color="Maroon" title="c1">R</font> is  <a href="wellord1.html#V1" title="WELLORD1:attr.1">well_founded</a>  &amp; <font color="Maroon" title="c3">F</font> <a href="wellord1.html#R3" title="WELLORD1:pred.3">is_isomorphism_of</a> <font color="Maroon" title="c1">R</font>,<font color="Maroon" title="c2">S</font> )
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="wellord1.html#D4" target="_self" title="WELLORD1:def.4">WELLORD1: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">S</font> is  <a href="wellord1.html#V2" title="WELLORD1:attr.2">well-ordering</a> </span><br/>

<span class="kw">hence </span><a NAME="E2:54"/>
( <font color="Maroon" title="c2">S</font> is  <a href="relat_2.html#V1" title="RELAT_2:attr.1">reflexive</a>  &amp; <font color="Maroon" title="c2">S</font> is  <a href="relat_2.html#V8" title="RELAT_2:attr.8">transitive</a>  &amp; <font color="Maroon" title="c2">S</font> is  <a href="relat_2.html#V4" title="RELAT_2:attr.4">antisymmetric</a>  &amp; <font color="Maroon" title="c2">S</font> is  <a href="relat_2.html#V6" title="RELAT_2:attr.6">connected</a>  &amp; <font color="Maroon" title="c2">S</font> is  <a href="wellord1.html#V1" title="WELLORD1:attr.1">well_founded</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="wellord1.html#T43" target="_self" title="WELLORD1:th.43">Th53</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="wellord1.html#D4" target="_self" title="WELLORD1:def.4">WELLORD1:def 4</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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