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<b>let </b><font color="Maroon">X1</font> be    <a href="hidden.html#M1">set</a> , <font color="Maroon">X2</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>given </b><font color="Maroon">L</font> being   <a href="ordinal1.html#NM3">T-Sequence</a><b> such that </b><a NAME="E1:1_1_2"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">X1</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">d</font> where <font color="Olive">d</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> : for <font color="Olive">d1</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font>  st <font color="Olive">d1</font> <a href="hidden.html#R2">in</a> <font color="Olive">d</font> holds <br/> ex <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Olive">B</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">L</font> &amp; <font color="Olive">d1</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="funct_1.html#K1">.</a> <font color="Olive">B</font></span>)</span></span><a href="tarski.html#K1">}</a></span> ) </span>}</span>  &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp; ( for <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Maroon">L</font> <a href="funct_1.html#K1">.</a> <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">d1</font> where <font color="Olive">d1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> : for <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font>  st <font color="Olive">d</font> <a href="hidden.html#R2">in</a> <font color="Olive">d1</font> holds <br/> ex <font color="Olive">C</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Olive">C</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="ordinal1.html#K2">|</a> <font color="Olive">B</font></span>)</span> &amp; <font color="Olive">d</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="ordinal1.html#K2">|</a> <font color="Olive">B</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">C</font></span>)</span></span><a href="tarski.html#K1">}</a></span> ) </span>}</span>  ) )
 ;<br/>

<b>given </b><font color="Maroon">L1</font> being   <a href="ordinal1.html#NM3">T-Sequence</a><b> such that </b><a NAME="E2:1_1_2"/><i><font color="Green">E38</font></i>: 
( <font color="Maroon">X2</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">d</font> where <font color="Olive">d</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> : for <font color="Olive">d1</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font>  st <font color="Olive">d1</font> <a href="hidden.html#R2">in</a> <font color="Olive">d</font> holds <br/> ex <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Olive">B</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">L1</font> &amp; <font color="Olive">d1</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">L1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">B</font></span>)</span></span><a href="tarski.html#K1">}</a></span> ) </span>}</span>  &amp;  <a href="relat_1.html#K1">dom</a> <font color="Maroon">L1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp; ( for <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a>  st <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> holds <br/><font color="Maroon">L1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">d1</font> where <font color="Olive">d1</font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font> : for <font color="Olive">d</font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">E</font>  st <font color="Olive">d</font> <a href="hidden.html#R2">in</a> <font color="Olive">d1</font> holds <br/> ex <font color="Olive">C</font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <br/>( <font color="Olive">C</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">L1</font> <a href="ordinal1.html#K2">|</a> <font color="Olive">B</font></span>)</span> &amp; <font color="Olive">d</font> <a href="hidden.html#R2">in</a>  <a href="tarski.html#K3">union</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L1</font> <a href="ordinal1.html#K2">|</a> <font color="Olive">B</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">C</font></span>)</span></span><a href="tarski.html#K1">}</a></span> ) </span>}</span>  ) )
 ;<br/>

<a NAME="E3:1_1_2"/><i><font color="Green">E39</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp; ( for <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a><br/> for <font color="Olive">L1</font> being  <a href="ordinal1.html#NM3">T-Sequence</a>  st <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Olive">L1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">L</font> <a href="ordinal1.html#K2">|</a> <font color="Olive">B</font> holds <br/><font color="Maroon">L</font> <a href="funct_1.html#K1">.</a> <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">L1</font>) ) )
 
<b>by </b><i/>;<br/>
<a NAME="E4:1_1_2"/><i><font color="Green">E40</font></i>: 
(  <a href="relat_1.html#K1">dom</a> <font color="Maroon">L1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A</font> &amp; ( for <font color="Olive">B</font> being  <a href="ordinal1.html#NM2">Ordinal</a><br/> for <font color="Olive">L</font> being  <a href="ordinal1.html#NM3">T-Sequence</a>  st <font color="Olive">B</font> <a href="hidden.html#R2">in</a> <font color="Maroon">A</font> &amp; <font color="Olive">L</font> <a href="hidden.html#R1">=</a> <font color="Maroon">L1</font> <a href="ordinal1.html#K2">|</a> <font color="Olive">B</font> holds <br/><font color="Maroon">L1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">B</font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">L</font>) ) )
 
<b>by </b><i/>;<br/>
<a NAME="E5:1_1_2"/>
<font color="Maroon">L</font> <a href="hidden.html#R1">=</a> <font color="Maroon">L1</font>
 
<b>from </b><i><a class="ref" href="ordinal1.html#S3">ORDINAL1:sch 3</a>(, );<br/></i>
<b>hence </b><a NAME="E6:1_1_2"/>
<font color="Maroon">X1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">X2</font>
 <b>by </b><i>, </i>;<br/>


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