<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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">R</font> being    <a href="mycielsk.html#M1" title="MYCIELSK:mode.1">NatRelStr</a> of <font color="Maroon" title="c1">n</font><br/>  for <font color="Olive" title="b2">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K6" title="MYCIELSK:func.6">Mycielskian</a> <font color="Olive" title="b1">R</font></span>)</span>  st <font color="Olive" title="b2">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Olive" title="b1">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Olive" title="b2">S</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font> be    <a href="mycielsk.html#M1" title="MYCIELSK:mode.1">NatRelStr</a> of <font color="Maroon" title="c1">n</font>; <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">S</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K6" title="MYCIELSK:func.6">Mycielskian</a> <font color="Maroon" title="c2">R</font></span>)</span>  st <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> holds <br/><font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Olive" title="b1">S</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">S</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K6" title="MYCIELSK:func.6">Mycielskian</a> <font color="Maroon" title="c2">R</font></span>)</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="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> implies <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:78"/><span class="lab"><font color="Green" title="E46">A1</font></span>: 
<font color="Maroon" title="c3">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</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="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c4">cR</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">iR</font> =  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">sS</font> =  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">csS</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">isS</font> =  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">MR</font> =  <a href="mycielsk.html#K6" title="MYCIELSK:func.6">Mycielskian</a> <font color="Maroon" title="c2">R</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">cMR</font> =  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K6" title="MYCIELSK:func.6">Mycielskian</a> <font color="Maroon" title="c2">R</font></span>)</span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">iMR</font> =  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K6" title="MYCIELSK:func.6">Mycielskian</a> <font color="Maroon" title="c2">R</font></span>)</span>;<br/>
<a NAME="E2:78"/><span class="lab"><font color="Green" title="E47">A2</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mycielsk.html#D7" target="_self" title="MYCIELSK:def.7">Def7</a></span>;<br/>
<a NAME="E3:78"/><span class="lab"><font color="Green" title="E48">A3</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:78"><span class="lab"><font color="Green" title="E46">A1</font></span></a>, <a class="ref" href="yellow_0.html#D15" title="YELLOW_0:def.15">YELLOW_0:def 15</a></span>;<br/>
<a NAME="E4:78"/><span class="lab"><font color="Green" title="E49">A4</font></span>: 
 the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">thus </span><a NAME="E1:78_1"/>
 the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span>
  <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R</font></span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c12">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R</font> or <font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:78_1_1"/><span class="lab"><font color="Green" title="E50">A5</font></span>: 
<font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">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="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">x</font>, <font color="Maroon" title="c14">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:78_1_1"/><span class="lab"><font color="Green" title="E51">A6</font></span>: 
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R</font>
 <span class="kw">and </span><br/><a NAME="E4:78_1_1"/><span class="lab"><font color="Green" title="E52">A7</font></span>: 
<font color="Maroon" title="c14">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R</font>
 <span class="kw">and </span><br/><a NAME="E5:78_1_1"/><span class="lab"><font color="Green" title="E53">A8</font></span>: 
<font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">x</font>,<font color="Maroon" title="c14">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/>
<a NAME="E6:78_1_1"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K6" title="MYCIELSK:func.6">Mycielskian</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mycielsk.html#T37" target="_self" title="MYCIELSK:th.37">Th37</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">xMR</font> = <font color="Maroon" title="c13">x</font>, <font color="Maroon" title="c16">yMR</font> = <font color="Maroon" title="c14">y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K6" title="MYCIELSK:func.6">Mycielskian</a> <font color="Maroon" title="c2">R</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78_1_1"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="txt" href="#E4:78_1_1"><span class="lab"><font color="Green" title="E52">A7</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">xsS</font> = <font color="Maroon" title="c13">x</font>, <font color="Maroon" title="c18">ysS</font> = <font color="Maroon" title="c14">y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78_1_1"><span class="lab"><font color="Green" title="E51">A6</font></span></a>, <a class="txt" href="#E4:78_1_1"><span class="lab"><font color="Green" title="E52">A7</font></span></a>, <a class="ref" href="mycielsk.html#D7" target="_self" title="MYCIELSK:def.7">Def7</a>, <a class="txt" href="#E3:78"><span class="lab"><font color="Green" title="E48">A3</font></span></a></span>;<br/>
<a NAME="E9:78_1_1"/>
 the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K6" title="MYCIELSK:func.6">Mycielskian</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mycielsk.html#T39" target="_self" title="MYCIELSK:th.39">Th39</a></span>;<br/>
<a NAME="E10:78_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c15">xMR</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">yMR</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:78_1_1"><span class="lab"><font color="Green" title="E50">A5</font></span></a>, <a class="txt" href="#E5:78_1_1"><span class="lab"><font color="Green" title="E53">A8</font></span></a>, <a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></span>;<br/>
<a NAME="E11:78_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c17">xsS</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c18">ysS</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="txt" href="#E2:78"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="txt" href="#E4:78_1_1"><span class="lab"><font color="Green" title="E52">A7</font></span></a>, <a class="ref" href="yellow_0.html#T60" title="YELLOW_0:th.60">YELLOW_0:60</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:78_1_1"/>
<font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:78_1_1"><span class="lab"><font color="Green" title="E53">A8</font></span></a>, <a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2: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/>


</div><span class="kw">end;</span></div>

<span class="kw">thus </span><a NAME="E2:78_1"/>
 the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R</font>
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="78_1_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c12">z</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span> or <font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:78_1_2"/><span class="lab"><font color="Green" title="E50">A9</font></span>: 
<font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</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="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c13">x</font>, <font color="Maroon" title="c14">y</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E3:78_1_2"/><span class="lab"><font color="Green" title="E51">A10</font></span>: 
<font color="Maroon" title="c13">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:78_1_2"/><span class="lab"><font color="Green" title="E52">A11</font></span>: 
<font color="Maroon" title="c14">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:78_1_2"/><span class="lab"><font color="Green" title="E53">A12</font></span>: 
<font color="Maroon" title="c12">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c13">x</font>,<font color="Maroon" title="c14">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#D2" title="ZFMISC_1:def.2">ZFMISC_1:def 2</a></span>;<br/>
<a NAME="E6:78_1_2"/>
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">R</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K6" title="MYCIELSK:func.6">Mycielskian</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mycielsk.html#T37" target="_self" title="MYCIELSK:th.37">Th37</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">xMR</font> = <font color="Maroon" title="c13">x</font>, <font color="Maroon" title="c16">yMR</font> = <font color="Maroon" title="c14">y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K6" title="MYCIELSK:func.6">Mycielskian</a> <font color="Maroon" title="c2">R</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78_1_2"><span class="lab"><font color="Green" title="E51">A10</font></span></a>, <a class="txt" href="#E4:78_1_2"><span class="lab"><font color="Green" title="E52">A11</font></span></a>, <a class="txt" href="#E2:78"><span class="lab"><font color="Green" title="E47">A2</font></span></a>, <a class="txt" href="#E3:78"><span class="lab"><font color="Green" title="E48">A3</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">xsS</font> = <font color="Maroon" title="c13">x</font>, <font color="Maroon" title="c18">ysS</font> = <font color="Maroon" title="c14">y</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78_1_2"><span class="lab"><font color="Green" title="E51">A10</font></span></a>, <a class="txt" href="#E4:78_1_2"><span class="lab"><font color="Green" title="E52">A11</font></span></a></span>;<br/>
<a NAME="E9:78_1_2"/>
<font color="Maroon" title="c17">xsS</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c18">ysS</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:78_1_2"><span class="lab"><font color="Green" title="E50">A9</font></span></a>, <a class="txt" href="#E5:78_1_2"><span class="lab"><font color="Green" title="E53">A12</font></span></a>, <a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></span>;<br/>
<a NAME="E10:78_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c15">xMR</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c16">yMR</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T59" title="YELLOW_0:th.59">YELLOW_0:59</a></span>;<br/>
<a NAME="E11:78_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="mycielsk.html#K6" title="MYCIELSK:func.6">Mycielskian</a> <font color="Maroon" title="c2">R</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:78_1_2"><span class="lab"><font color="Green" title="E53">A12</font></span></a>, <a class="ref" href="orders_2.html#D5" title="ORDERS_2:def.5">ORDERS_2:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:78_1_2"/>
<font color="Maroon" title="c12">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">R</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:78_1_2"><span class="lab"><font color="Green" title="E51">A10</font></span></a>, <a class="txt" href="#E4:78_1_2"><span class="lab"><font color="Green" title="E52">A11</font></span></a>, <a class="txt" href="#E3:78"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="txt" href="#E5:78_1_2"><span class="lab"><font color="Green" title="E53">A12</font></span></a>, <a class="ref" href="mycielsk.html#T40" target="_self" title="MYCIELSK:th.40">Th40</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/>


</div><span class="kw">end;</span></div>


</div><span class="kw">end;</span></div>
<span class="kw">thus </span><a NAME="E5:78"/>
<font color="Maroon" title="c2">R</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c3">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mycielsk.html#D7" target="_self" title="MYCIELSK:def.7">Def7</a>, <a class="txt" href="#E3:78"><span class="lab"><font color="Green" title="E48">A3</font></span></a>, <a class="txt" href="#E4:78"><span class="lab"><font color="Green" title="E49">A4</font></span></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/>


</div>
