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<b>consider </b><font color="Maroon">c<sub>5</sub></font> being   <a href="ordinal1.html#NM3">T-Sequence</a><b> such that </b><br/><a NAME="E2:50_1_1"/><i><font color="Green">E26</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E3:50_1_1"/><i><font color="Green">E27</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>3</sub></font> holds <br/><font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>from </b><i><a class="ref" href="ordinal2.html#S2">ORDINAL2:sch 2</a>();<br/></i>
<b>take </b>
<font color="Maroon">c<sub>5</sub></font>
;<br/>

<b>thus </b><a NAME="E4:50_1_1"/>
<font color="Maroon">c<sub>5</sub></font> is    <a href="ordinal1.html#M1">T-Sequence</a> of the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="50_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a>,<a class="ref" href="ordinal1.html#D8">ORDINAL1:def 8</a><br/>

<b>assume </b><a NAME="E1:50_1_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>5</sub></font>
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>7</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:50_1_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font>
 <b>and </b><br/><a NAME="E4:50_1_1_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<a NAME="E5:50_1_1_1"/>
<font color="Maroon">c<sub>7</sub></font> is   <a href="ordinal1.html#NM2">Ordinal</a>
 
<b>by </b><i><a class="txt" href="amistd_3.html#E3:50_1_1_1"><i><font color="Green">E28</font></i></a>, <a class="ref" href="ordinal1.html#T23">ORDINAL1:23</a></i>;<br/>
<a NAME="E6:50_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon">c<sub>7</sub></font>)
 
<b>by </b><i><a class="txt" href="amistd_3.html#E2:50_1_1"><i><font color="Green">E26</font></i></a>, <a class="txt" href="amistd_3.html#E3:50_1_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="amistd_3.html#E3:50_1_1_1"><i><font color="Green">E28</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:50_1_1_1"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> the <a href="ami_1.html#U2">Instruction-Locations</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="amistd_3.html#E4:50_1_1_1"><i><font color="Green">E29</font></i></a></i>;<br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E5:50_1_1"/>
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="amistd_3.html#E2:50_1_1"><i><font color="Green">E26</font></i></a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E6:50_1_1"/><i><font color="Green">E28</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a>  <a href="card_1.html#K1">Card</a> <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<a NAME="E7:50_1_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> is   <a href="ordinal1.html#NM2">Ordinal</a>
 
<b>by </b><i><a class="ref" href="ordinal1.html#T23">ORDINAL1:23</a></i>;<br/>
<b>hence </b><a NAME="E8:50_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a>  <a href="amistd_1.html#K5">il.</a> <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="wellord1.html#K3">canonical_isomorphism_of</a> <span class="p3">(<span class="default"><a href="wellord2.html#K1">RelIncl</a> <span class="p4">(<span class="default"><a href="wellord2.html#K2">order_type_of</a> <span class="p5">(<span class="default"><a href="wellord2.html#K1">RelIncl</a> <span class="p0">(<span class="default"><a href="amistd_3.html#K3" target="_self">LocNums</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>,<span class="p3">(<span class="default"><a href="wellord2.html#K1">RelIncl</a> <span class="p4">(<span class="default"><a href="amistd_3.html#K3" target="_self">LocNums</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="amistd_3.html#E3:50_1_1"><i><font color="Green">E27</font></i></a>, <a class="txt" href="amistd_3.html#E6:50_1_1"><i><font color="Green">E28</font></i></a></i>;<br/>


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