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

<a NAME="E1:77_1"/><i><font color="Green" title="E39">A3</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<br/> for <font color="Olive" title="b4">f</font>, <font color="Olive" title="b5">g</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>  st <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">f</font>] &amp; <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b5">g</font>] holds <br/><font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b5">g</font> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <font color="Olive" title="b4">f</font>]
 
<b>by </b><i><a class="txt" href="yellow18.html#E1:77"><i><font color="Green" title="E37">A1</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c1">D</font> being   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a><b> such that </b><br/><a NAME="E3:77_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <font color="Maroon" title="c1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>and </b><br/><a NAME="E4:77_1"/><i><font color="Green" title="E40">A4</font></i>: 
for <font color="Olive" title="b1">a</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>1</sub></font>() holds <br/>for <font color="Olive" title="b2">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">a</font> iff ( <font color="Olive" title="b2">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive" title="b1">a</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">y</font>] ) )
 <b>from </b><i><a class="ref" href="card_3.html#S4" title="CARD_3:sch.4">CARD_3:sch 4</a>();<br/></i>
<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ) <b>-&gt; </b>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  = <font color="Maroon" title="c1">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> $1;<br/>
<div><i><font color="Green" title="E41">A5</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="77_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c2">a</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><a NAME="E1:77_1_1"/>
for <font color="Olive" title="b1">y</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">a</font> iff ( <font color="Olive" title="b1">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c2">a</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">y</font>] ) )
 <b>by </b><i><a class="txt" href="yellow18.html#E4:77_1"><i><font color="Green" title="E40">A4</font></i></a></i>;<br/><b>hence </b><a NAME="E2:77_1_1"/>
<font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c2">a</font>, <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c2">a</font>)]
 <b>by </b><i><a class="txt" href="yellow18.html#E2:77"><i><font color="Green" title="E38">A2</font></i></a></i>;<br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c2">C</font> being  <a href="altcat_1.html#V6" title="ALTCAT_1:attr.6">strict</a> <a href="altcat_1.html#V9" title="ALTCAT_1:attr.9">semi-functional</a> <a href="yellow18.html#V2" title="YELLOW18:attr.2">para-functional</a> <a href="yellow18.html#V3" title="YELLOW18:attr.3">set-id-inheriting</a> <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a><b> such that </b><br/><a NAME="E7:77_1"/><i><font color="Green" title="E42">A6</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>and </b><br/><a NAME="E8:77_1"/><i><font color="Green" title="E43">A7</font></i>: 
for <font color="Olive" title="b1">a</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">C</font> holds   <a href="yellow18.html#K3" title="YELLOW18:func.3">the_carrier_of</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">a</font>)
 <b>and </b><br/><a NAME="E9:77_1"/><i><font color="Green" title="E44">A8</font></i>: 
for <font color="Olive" title="b1">a</font>, <font color="Olive" title="b2">b</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>()<br/> for <font color="Olive" title="b3">f</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds <br/> ( <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">C</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font> iff ( <font color="Olive" title="b3">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">a</font>),<font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b2">b</font>) &amp; <font color="Maroon">P<sub>2</sub></font>[<font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">f</font>] ) )
 <b>from </b><i><a class="ref" href="yellow18.html#S17" target="_self" title="YELLOW18:sch.17">YELLOW18:sch 17</a>(<a class="txt" href="yellow18.html#E1:77_1"><i><font color="Green" title="E39">A3</font></i></a>, <a class="txt" href="yellow18.html#E5:77_1"><i><font color="Green" title="E41">A5</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon" title="c2">C</font>
;<br/>

<b>thus </b><a NAME="E10:77_1"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>1</sub></font>()
 <b>by </b><i><a class="txt" href="yellow18.html#E7:77_1"><i><font color="Green" title="E42">A6</font></i></a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c3">a</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">C</font>;<br/><a NAME="E1:77_1_2"/>
 <a href="yellow18.html#K3" title="YELLOW18:func.3">the_carrier_of</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font>
 <b>by </b><i><a class="txt" href="yellow18.html#E8:77_1"><i><font color="Green" title="E43">A7</font></i></a></i>;<br/><b>hence </b><a NAME="E2:77_1_2"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="yellow18.html#K3" title="YELLOW18:func.3">the_carrier_of</a> <font color="Maroon" title="c3">a</font> iff ( <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon" title="c3">a</font>) &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon" title="c3">a</font>,<font color="Olive" title="b1">x</font>] ) )
 <b>by </b><i><a class="txt" href="yellow18.html#E4:77_1"><i><font color="Green" title="E40">A4</font></i></a>, <a class="txt" href="yellow18.html#E7:77_1"><i><font color="Green" title="E42">A6</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/>

<a NAME="E12:77_1"/>
( <font color="Maroon" title="c1">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font> <a href="yellow18.html#K3" title="YELLOW18:func.3">-carrier_of</a> <font color="Maroon" title="c3">a</font> &amp; <font color="Maroon" title="c1">D</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">C</font> <a href="yellow18.html#K3" title="YELLOW18:func.3">-carrier_of</a> <font color="Maroon" title="c4">b</font> )
 
<b>by </b><i><a class="txt" href="yellow18.html#E7:77_1"><i><font color="Green" title="E42">A6</font></i></a>, <a class="txt" href="yellow18.html#E8:77_1"><i><font color="Green" title="E43">A7</font></i></a></i>;<br/>
<b>hence </b><a NAME="E13:77_1"/>
for <font color="Olive" title="b1">f</font> being  <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a> holds <br/> ( <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="altcat_1.html#U1" title="ALTCAT_1:sel.1">Arrows</a> of <font color="Maroon" title="c2">C</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font> iff ( <font color="Olive" title="b1">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="funct_2.html#K1" title="FUNCT_2:func.1">Funcs</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="yellow18.html#K3" title="YELLOW18:func.3">-carrier_of</a> <font color="Maroon" title="c3">a</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">C</font> <a href="yellow18.html#K3" title="YELLOW18:func.3">-carrier_of</a> <font color="Maroon" title="c4">b</font></span>)</span> &amp; <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Olive" title="b1">f</font>] ) )
 <b>by </b><i><a class="txt" href="yellow18.html#E9:77_1"><i><font color="Green" title="E44">A8</font></i></a></i>;<br/>


</div>
