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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="lattices.html#NM1">Lattice</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="funct_2.html#NM1">Function</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="ordinal1.html#NM2">Ordinal</a>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="ordinal1.html#NM3">T-Sequence</a>;<br/>









<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="ordinal1.html#NM2">Ordinal</a>,   <a href="hidden.html#M1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">a<sub>2</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>2</sub></font>(  <a href="ordinal1.html#NM2">Ordinal</a>,  <a href="ordinal1.html#NM3">T-Sequence</a>) <b>-&gt; </b>   <a href="subset_1.html#M1">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> =  <a href="lattice3.html#K15">"\/"</a> <span class="p1">(<span class="default"><a href="relat_1.html#K2">rng</a> <font color="Maroon">a<sub>2</sub></font></span>)</span>,<font color="Maroon">c<sub>1</sub></font>;<br/>
<b>deffunc </b><font color="Maroon">H<sub>3</sub></font>(  <a href="ordinal1.html#NM2">Ordinal</a>) <b>-&gt; </b>   <a href="hidden.html#M1">set</a>  = <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">a<sub>1</sub></font> <a href="knaster.html#K3" target="_self">+.</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>assume </b><b>that </b><br/><a NAME="E1:23"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a>  )
 <b>and </b><br/><a NAME="E2:23"/><i><font color="Green">E20</font></i>: 
 <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font>
 <b>and </b><br/><a NAME="E3:23"/><i><font color="Green">E21</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> <font color="Maroon">c<sub>4</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>3</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 ;<br/>

<a NAME="E4:23"/><i><font color="Green">E22</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a><br/>for <font color="Olive">b<sub>2</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) iff ex <font color="Olive">b<sub>3</sub></font> being  <a href="ordinal1.html#NM3">T-Sequence</a> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="ordinal2.html#K1">last</a> <font color="Olive">b<sub>3</sub></font> &amp;  <a href="relat_1.html#K1">dom</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="ordinal1.html#K1">succ</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> &amp; ( for <font color="Olive">b<sub>4</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> st  <a href="ordinal1.html#K1">succ</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K1">succ</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="ordinal1.html#K1">succ</a> <font color="Olive">b<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>4</sub></font>) ) &amp; ( for <font color="Olive">b<sub>4</sub></font> being  <a href="ordinal1.html#NM2">Ordinal</a> st <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="ordinal1.html#K1">succ</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Olive">b<sub>4</sub></font> <a href="ordinal1.html#NR2" target="_self">is_limit_ordinal</a>  holds <br/><font color="Olive">b<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>3</sub></font> <a href="ordinal1.html#K2">|</a> <font color="Olive">b<sub>4</sub></font>) ) ) )
 
<b>by </b><i><a class="ref" href="knaster.html#D6" target="_self">Def6</a></i>;<br/>
<b>thus </b><a NAME="E5:23"/>
<font color="Maroon">H<sub>3</sub></font>(<font color="Maroon">c<sub>4</sub></font>) <a href="hidden.html#R1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>)
 <b>from </b><i><a class="ref" href="ordinal2.html#S10">ORDINAL2:sch 10</a>(<a class="txt" href="knaster.html#E4:23"><i><font color="Green">E22</font></i></a>, <a class="txt" href="knaster.html#E1:23"><i><font color="Green">E19</font></i></a>, <a class="txt" href="knaster.html#E2:23"><i><font color="Green">E20</font></i></a>, <a class="txt" href="knaster.html#E3:23"><i><font color="Green">E21</font></i></a>);</i><br/>


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