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

<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  <a href="altcat_1.html#V6">strict</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:37_1"/><i><font color="Green">E19</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() holds <br/>( the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>1</sub></font> <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>) &amp; ( for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() holds the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>1</sub></font> <a href="multop_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="altcat_1.html#K6">FuncComp</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font>) ) ) ) )
 <b>and </b><br/><a NAME="E2:37_1"/><i><font color="Green">E20</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>1</sub></font>() &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() holds <br/>( the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>) &amp; ( for <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being   <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() holds the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>2</sub></font> <a href="multop_1.html#K1">.</a> <font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="altcat_1.html#K6">FuncComp</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font>) ) ) ) )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>thus </b>the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>1</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font> = 
<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>)
<b>by </b><i><a class="txt" href="orders_3.html#E1:37_1"><i><font color="Green">E19</font></i></a></i>
<br/>.= 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>2</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="orders_3.html#E2:37_1"><i><font color="Green">E20</font></i></a></i>
;<br/></div><b>end;</b></div>
<a NAME="E4:37_1"/><b>then </b><i><font color="Green">E21</font></i>: 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="orders_3.html#E1:37_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="orders_3.html#E2:37_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="altcat_1.html#T9">ALTCAT_1:9</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:37_1_2"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">F<sub>1</sub></font>() )
 ;<br/><b>hence </b>the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>1</sub></font> <a href="multop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font> = 
 <a href="altcat_1.html#K6">FuncComp</a> <font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>),<font color="Maroon">F<sub>2</sub></font>(<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>)
<b>by </b><i><a class="txt" href="orders_3.html#E1:37_1"><i><font color="Green">E19</font></i></a></i>
<br/>.= 
the <a href="altcat_1.html#U2">Comp</a> of <font color="Maroon">c<sub>2</sub></font> <a href="multop_1.html#K1">.</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="orders_3.html#E2:37_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="orders_3.html#E1:37_1_2"><i><font color="Green">E22</font></i></a></i>
;<br/><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E6:37_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="orders_3.html#E1:37_1"><i><font color="Green">E19</font></i></a>, <a class="txt" href="orders_3.html#E2:37_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="orders_3.html#E4:37_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="altcat_1.html#T10">ALTCAT_1:10</a></i>;<br/>


</div>
