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

<a NAME="E1:23_1"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>1</sub></font>() holds <font color="Maroon">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>) is   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>2</sub></font>()
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>1</sub></font>();<br/>

<a NAME="E1:23_1_1"/>
( <font color="Maroon">c<sub>1</sub></font> is   <a href="waybel_0.html#NM8">LATTICE</a> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() )
 
<b>by </b><i><a class="ref" href="yellow21.html#D4" target="_self">Def4</a></i>;<br/>
<b>hence </b><a NAME="E2:23_1_1"/>
<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) is   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>2</sub></font>()
 <b>by </b><i><a class="txt" href="yellow21.html#E3:23"><i><font color="Green">E11</font></i></a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E2:23_1"/><i><font color="Green">E16</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>1</sub></font>() st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds <font color="Maroon">F<sub>4</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>) <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">F<sub>2</sub></font>() <a href="binop_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>),<font color="Maroon">F<sub>3</sub></font>(<font color="Olive">b<sub>2</sub></font>)
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_2"><b>proof </b></a><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#NM1">object</a> of <font color="Maroon">F<sub>1</sub></font>();<br/>

<b>assume </b><a NAME="E1:23_1_2"/><i><font color="Green">E17</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>

<a NAME="E2:23_1_2"/><i><font color="Green">E18</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K5" target="_self">@</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>2</sub></font> )
 
<b>by </b><i><a class="txt" href="yellow21.html#E1:23_1_2"><i><font color="Green">E17</font></i></a>, <a class="ref" href="yellow21.html#D7" target="_self">Def7</a></i>;<br/>
<a NAME="E3:23_1_2"/>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>] )
 
<b>by </b><i><a class="txt" href="yellow21.html#E1:23"><i><font color="Green">E9</font></i></a>, <a class="txt" href="yellow21.html#E1:23_1_2"><i><font color="Green">E17</font></i></a>, <a class="txt" href="yellow21.html#E2:23_1_2"><i><font color="Green">E18</font></i></a></i>;<br/>
<a NAME="E4:23_1_2"/><b>then </b>
( <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>) <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>() &amp; <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>) is   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>) &amp; <font color="Maroon">P<sub>2</sub></font>[<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>),<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>)] )
 
<b>by </b><i><a class="txt" href="yellow21.html#E3:23"><i><font color="Green">E11</font></i></a>, <a class="txt" href="yellow21.html#E4:23"><i><font color="Green">E12</font></i></a>, <a class="txt" href="yellow21.html#E2:23_1_2"><i><font color="Green">E18</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:23_1_2"/>
<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>) <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">F<sub>2</sub></font>() <a href="binop_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>)
 <b>by </b><i><a class="txt" href="yellow21.html#E2:23"><i><font color="Green">E10</font></i></a></i>;<br/>


</div><b>end;</b></div>
<div><i><font color="Green">E17</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_3"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>assume </b><a NAME="E1:23_1_3"/><i><font color="Green">E18</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font>, <font color="Maroon">c<sub>8</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>2</sub></font>();<br/><b>assume </b><a NAME="E2:23_1_3"/><i><font color="Green">E19</font></i>: 
( <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) &amp; <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>) &amp; <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>3</sub></font>) )
 ;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font>;<br/><b>assume </b><a NAME="E3:23_1_3"/><i><font color="Green">E20</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>) &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>) )
 ;<br/><a NAME="E4:23_1_3"/><i><font color="Green">E21</font></i>: 
(  <a href="yellow21.html#K5" target="_self">@</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>4</sub></font> &amp;  <a href="yellow21.html#K5" target="_self">@</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="yellow21.html#E1:23_1_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="yellow21.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E5:23_1_3"/>
(  <a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> &amp;  <a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>) <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">F<sub>2</sub></font>() <a href="binop_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>),<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>) &amp; <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>) <a href="hidden.html#R2">in</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">F<sub>2</sub></font>() <a href="binop_1.html#K1">.</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>2</sub></font>),<font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>3</sub></font>) )
 <b>by </b><i><a class="txt" href="yellow21.html#E2:23_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="yellow21.html#E1:23_1_3"><i><font color="Green">E18</font></i></a></i>;<br/><a NAME="E6:23_1_3"/><b>then </b><i><font color="Green">E22</font></i>: 
( <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>) <a href="hidden.html#R2">in</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> &amp; <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>) <a href="hidden.html#R2">in</a> <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> )
 <b>by </b><i><a class="txt" href="yellow21.html#E2:23_1_3"><i><font color="Green">E19</font></i></a></i>;<br/><a NAME="E7:23_1_3"/><b>then </b><i><font color="Green">E23</font></i>: 
(  <a href="yellow21.html#K5" target="_self">@</a> <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> &amp;  <a href="yellow21.html#K5" target="_self">@</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="ref" href="yellow21.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E8:23_1_3"/>
( <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>] &amp; <font color="Maroon">P<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>] )
 <b>by </b><i><a class="txt" href="yellow21.html#E1:23"><i><font color="Green">E9</font></i></a>, <a class="txt" href="yellow21.html#E1:23_1_3"><i><font color="Green">E18</font></i></a>, <a class="txt" href="yellow21.html#E4:23_1_3"><i><font color="Green">E21</font></i></a></i>;<br/><b>then </b><font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="yellow21.html#K5" target="_self">@</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="yellow21.html#K5" target="_self">@</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>) = 
<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>) <a href="funct_1.html#NK3" target="_self">*</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>4</sub></font>)
<b>by </b><i><a class="txt" href="yellow21.html#E6:23"><i><font color="Green">E14</font></i></a>, <a class="txt" href="yellow21.html#E4:23_1_3"><i><font color="Green">E21</font></i></a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>9</sub></font>
<b>by </b><i><a class="txt" href="yellow21.html#E3:23_1_3"><i><font color="Green">E20</font></i></a>, <a class="txt" href="yellow21.html#E6:23_1_3"><i><font color="Green">E22</font></i></a>, <a class="txt" href="yellow21.html#E7:23_1_3"><i><font color="Green">E23</font></i></a>, <a class="ref" href="yellow21.html#T3" target="_self">Th3</a></i>
;<br/><b>hence </b><a NAME="E10:23_1_3"/>
<font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>) <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>10</sub></font> <a href="altcat_1.html#K5">*</a> <font color="Maroon">c<sub>9</sub></font>
 <b>by </b><i><a class="txt" href="yellow21.html#E1:23_1_3"><i><font color="Green">E18</font></i></a>, <a class="ref" href="yellow21.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div>
<div><i><font color="Green">E18</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>1</sub></font>();<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>2</sub></font>();<br/><b>assume </b><a NAME="E1:23_1_4"/>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>)
 ;<br/><a NAME="E2:23_1_4"/><b>then </b>
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>() &amp;  <a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Maroon">c<sub>1</sub></font>) &amp;  <a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="grcat_1.html#K7">id</a> <span class="p1">(<span class="default"><a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="yellow21.html#T2" target="_self">Th2</a></i>;<br/><b>hence </b><font color="Maroon">F<sub>4</sub></font>(<font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>) = 
 <a href="grcat_1.html#K7">id</a> <span class="p1">(<span class="default"><a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="yellow21.html#E5:23"><i><font color="Green">E13</font></i></a></i>
<br/>.= 
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="ref" href="yellow21.html#T2" target="_self">Th2</a></i>
;<br/><br/></div><b>end;</b></div>
<b>consider </b><font color="Maroon">c<sub>1</sub></font> being  <a href="functor0.html#V9">strict</a> <a href="functor0.html#V15">covariant</a>  <a href="functor0.html#M2">Functor</a> of <font color="Maroon">F<sub>1</sub></font>(),<font color="Maroon">F<sub>2</sub></font>()<b> such that </b><br/><a NAME="E6:23_1"/><i><font color="Green">E19</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>1</sub></font>() holds <font color="Maroon">c<sub>1</sub></font> <a href="functor0.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>(<font color="Olive">b<sub>1</sub></font>)
 <b>and </b><br/><a NAME="E7:23_1"/><i><font color="Green">E20</font></i>: 
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>1</sub></font>() st <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  holds <br/>for <font color="Olive">b<sub>3</sub></font> being  <a href="altcat_1.html#NM2">Morphism</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> holds <font color="Maroon">c<sub>1</sub></font> <a href="functor0.html#K6">.</a> <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>(<font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>)
 <b>from </b><i><a class="ref" href="yellow18.html#S8">YELLOW18:sch 8</a>(<a class="txt" href="yellow21.html#E1:23_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="yellow21.html#E2:23_1"><i><font color="Green">E16</font></i></a>, <a class="txt" href="yellow21.html#E3:23_1"><i><font color="Green">E17</font></i></a>, <a class="txt" href="yellow21.html#E4:23_1"><i><font color="Green">E18</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon">c<sub>1</sub></font>
;<br/>

<b>thus </b><a NAME="E8:23_1"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>1</sub></font>() holds <font color="Maroon">c<sub>1</sub></font> <a href="functor0.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>3</sub></font>(<span class="p1">(<span class="default"><a href="yellow21.html#K3" target="_self">latt</a> <font color="Olive">b<sub>1</sub></font></span>)</span>)
 <b>by </b><i><a class="txt" href="yellow21.html#E6:23_1"><i><font color="Green">E19</font></i></a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">F<sub>1</sub></font>();<br/>

<b>assume </b><a NAME="E9:23_1"/><i><font color="Green">E21</font></i>: 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font></span><a href="altcat_1.html#K1">^&gt;</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="altcat_1.html#NM2">Morphism</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>

<a NAME="E10:23_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="yellow21.html#K5" target="_self">@</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="yellow21.html#E9:23_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="yellow21.html#D7" target="_self">Def7</a></i>;<br/>
<b>hence </b><a NAME="E11:23_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="functor0.html#K6">.</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">F<sub>4</sub></font>(<span class="p1">(<span class="default"><a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow21.html#K3" target="_self">latt</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow21.html#K5" target="_self">@</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>)
 <b>by </b><i><a class="txt" href="yellow21.html#E7:23_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="yellow21.html#E9:23_1"><i><font color="Green">E21</font></i></a></i>;<br/>


</div>
