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

<b>let </b><font color="Maroon" title="c1">A1</font>, <font color="Maroon" title="c2">A2</font>, <font color="Maroon" title="c3">A3</font> be   <a href="altcat_1.html#NM4" title="ALTCAT_1:NM.4">category</a>;<br/><b>let </b><font color="Maroon" title="c4">F</font> be  <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A1</font>,<font color="Maroon" title="c2">A2</font>;<br/><b>let </b><font color="Maroon" title="c5">G</font> be  <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c2">A2</font>,<font color="Maroon" title="c3">A3</font>;<br/><b>let </b><font color="Maroon" title="c6">B1</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A1</font>;<br/><b>let </b><font color="Maroon" title="c7">B2</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">A2</font>;<br/><b>let </b><font color="Maroon" title="c8">B3</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c3">A3</font>;<br/>











<b>assume </b><a NAME="E1:67"/>
( <font color="Maroon" title="c6">B1</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A1</font> &amp; <font color="Maroon" title="c7">B2</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">A2</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow20.html#D4" target="_self" title="YELLOW20:def.4">YELLOW20:def 4</a><br/>

<b>given </b><font color="Maroon" title="c9">F1</font> being  <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c6">B1</font>,<font color="Maroon" title="c7">B2</font><b> such that </b><a NAME="E3:67"/><i><font color="Green" title="E36">A1</font></i>: 
<font color="Maroon" title="c9">F1</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>
 <b>and </b><br/><a NAME="E4:67"/><i><font color="Green" title="E37">A2</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="c6">B1</font><br/> for <font color="Olive" title="b2">a1</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A1</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a1</font> holds <br/><font color="Maroon" title="c9">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b2">a1</font>
 <b>and </b><br/><a NAME="E5:67"/><i><font color="Green" title="E38">A3</font></i>: 
for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">c</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c6">B1</font><br/> for <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">c1</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A1</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b1</font> &amp; <font color="Olive" title="b2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">c1</font> holds <br/>for <font color="Olive" title="b5">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font><br/> for <font color="Olive" title="b6">f1</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">c1</font>  st <font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">f1</font> holds <br/><font color="Maroon" title="c9">F1</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c4">F</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">f1</font>
 ;<br/>

<b>assume </b><a NAME="E6:67"/>
( <font color="Maroon" title="c7">B2</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c2">A2</font> &amp; <font color="Maroon" title="c8">B3</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c3">A3</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow20.html#D4" target="_self" title="YELLOW20:def.4">YELLOW20:def 4</a><br/>

<b>given </b><font color="Maroon" title="c10">G1</font> being  <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>  <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c7">B2</font>,<font color="Maroon" title="c8">B3</font><b> such that </b><a NAME="E8:67"/><i><font color="Green" title="E39">A4</font></i>: 
<font color="Maroon" title="c10">G1</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>
 <b>and </b><br/><a NAME="E9:67"/><i><font color="Green" title="E40">A5</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="c7">B2</font><br/> for <font color="Olive" title="b2">a1</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>  st <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">a1</font> holds <br/><font color="Maroon" title="c10">G1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b1">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Olive" title="b2">a1</font>
 <b>and </b><br/><a NAME="E10:67"/><i><font color="Green" title="E41">A6</font></i>: 
for <font color="Olive" title="b1">b</font>, <font color="Olive" title="b2">c</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c7">B2</font><br/> for <font color="Olive" title="b3">b1</font>, <font color="Olive" title="b4">c1</font> being  <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">A2</font>  st <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Olive" title="b1">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">b1</font> &amp; <font color="Olive" title="b2">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b4">c1</font> holds <br/>for <font color="Olive" title="b5">f</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b1">b</font>,<font color="Olive" title="b2">c</font><br/> for <font color="Olive" title="b6">f1</font> being  <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">c1</font>  st <font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b6">f1</font> holds <br/><font color="Maroon" title="c10">G1</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Olive" title="b5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c5">G</font>,<font color="Olive" title="b3">b1</font>,<font color="Olive" title="b4">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b6">f1</font>
 ;<br/>

<b>thus </b><a NAME="E11:67"/>
( <font color="Maroon" title="c6">B1</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c1">A1</font> &amp; <font color="Maroon" title="c8">B3</font> is   <a href="altcat_2.html#NM2" title="ALTCAT_2:NM.2">subcategory</a> of <font color="Maroon" title="c3">A3</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow20.html#D4" target="_self" title="YELLOW20:def.4">YELLOW20:def 4</a><br/>

<b>take </b>
<font color="Maroon" title="c10">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c9">F1</font>
;<br/>

<b>thus </b><a NAME="E12:67"/>
<font color="Maroon" title="c10">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c9">F1</font> is <a href="functor0.html#V21" title="FUNCTOR0:attr.21">bijective</a>
 <b>by </b><i><a class="txt" href="yellow20.html#E3:67"><i><font color="Green" title="E36">A1</font></i></a>, <a class="txt" href="yellow20.html#E8:67"><i><font color="Green" title="E39">A4</font></i></a>, <a class="ref" href="functor1.html#T13" title="FUNCTOR1:th.13">FUNCTOR1:13</a></i>;<br/>

<div><b>hereby </b>
<div class="add"><b>let </b><font color="Maroon" title="c11">a</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c6">B1</font>;<br/><b>let </b><font color="Maroon" title="c12">b</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A1</font>;<br/><b>assume </b><a NAME="E1:67_1"/>
<font color="Maroon" title="c11">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">b</font>
 ;<br/><a NAME="E2:67_1"/><b>then </b>
<font color="Maroon" title="c9">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">b</font>
 <b>by </b><i><a class="txt" href="yellow20.html#E4:67"><i><font color="Green" title="E37">A2</font></i></a></i>;<br/><a NAME="E3:67_1"/><b>then </b>
<font color="Maroon" title="c10">G1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">a</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">b</font></span>)</span>
 <b>by </b><i><a class="txt" href="yellow20.html#E9:67"><i><font color="Green" title="E40">A5</font></i></a></i>;<br/><b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c10">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c9">F1</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">a</font> = 
<font color="Maroon" title="c5">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">b</font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#T34" title="FUNCTOR0:th.34">FUNCTOR0:34</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">b</font>
<b>by </b><i><a class="ref" href="functor0.html#T34" title="FUNCTOR0:th.34">FUNCTOR0:34</a></i>
;<br/><br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c11">b</font>, <font color="Maroon" title="c12">c</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c6">B1</font>;<br/><b>let </b><font color="Maroon" title="c13">b1</font>, <font color="Maroon" title="c14">c1</font> be   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c1">A1</font>;<br/>



<b>assume </b><a NAME="E14:67"/><i><font color="Green" title="E42">A7</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c11">b</font>,<font color="Maroon" title="c12">c</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">b1</font> &amp; <font color="Maroon" title="c12">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c14">c1</font> )
 ;<br/>

<b>let </b><font color="Maroon" title="c15">f</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c11">b</font>,<font color="Maroon" title="c12">c</font>;<br/><b>let </b><font color="Maroon" title="c16">f1</font> be   <a href="altcat_1.html#NM2" title="ALTCAT_1:NM.2">Morphism</a> of <font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c14">c1</font>;<br/>



<a NAME="E15:67"/><i><font color="Green" title="E43">A8</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">c</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <font color="Maroon" title="c9">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c13">b1</font> &amp; <font color="Maroon" title="c9">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c14">c1</font> )
 
<b>by </b><i><a class="txt" href="yellow20.html#E4:67"><i><font color="Green" title="E37">A2</font></i></a>, <a class="txt" href="yellow20.html#E14:67"><i><font color="Green" title="E42">A7</font></i></a>, <a class="ref" href="functor0.html#D19" title="FUNCTOR0:def.19">FUNCTOR0:def 19</a></i>;<br/>
<a NAME="E16:67"/><b>then </b><i><font color="Green" title="E44">A9</font></i>: 
( <font color="Maroon" title="c15">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c11">b</font>,<font color="Maroon" title="c12">c</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c11">b</font>,<font color="Maroon" title="c12">c</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c14">c1</font></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> &amp; <font color="Maroon" title="c9">F1</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c15">f</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">c</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> &amp; <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c9">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c11">b</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c9">F1</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c12">c</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c13">b1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c14">c1</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="yellow20.html#E14:67"><i><font color="Green" title="E42">A7</font></i></a>, <a class="ref" href="altcat_2.html#T32" title="ALTCAT_2:th.32">ALTCAT_2:32</a></i>;<br/>
<a NAME="E17:67"/><b>then </b><i><font color="Green" title="E45">A10</font></i>: 
( <span class="p1"><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c13">b1</font></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c14">c1</font></span>)</span></span><a href="altcat_1.html#K1" title="ALTCAT_1:func.1">^&gt;</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c13">b1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c13">b1</font></span>)</span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c14">c1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">G</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c14">c1</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="functor0.html#T34" title="FUNCTOR0:th.34">FUNCTOR0:34</a>, <a class="ref" href="functor0.html#D19" title="FUNCTOR0:def.19">FUNCTOR0:def 19</a></i>;<br/>
<b>assume </b><a NAME="E18:67"/>
<font color="Maroon" title="c15">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c16">f1</font>
 ;<br/>

<b>then </b><font color="Maroon" title="c9">F1</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c15">f</font> = 
<span class="p1">(<span class="default"><a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c14">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">f1</font>
<b>by </b><i><a class="txt" href="yellow20.html#E5:67"><i><font color="Green" title="E38">A3</font></i></a>, <a class="txt" href="yellow20.html#E14:67"><i><font color="Green" title="E42">A7</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c4">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c16">f1</font>
<b>by </b><i><a class="txt" href="yellow20.html#E16:67"><i><font color="Green" title="E44">A9</font></i></a>, <a class="ref" href="functor0.html#D16" title="FUNCTOR0:def.16">FUNCTOR0:def 16</a></i>
;<br/>
<a NAME="E20:67"/><b>then </b>
<font color="Maroon" title="c10">G1</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">F1</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c15">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c5">G</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c13">b1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c14">c1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c16">f1</font></span>)</span>
 
<b>by </b><i><a class="txt" href="yellow20.html#E10:67"><i><font color="Green" title="E41">A6</font></i></a>, <a class="txt" href="yellow20.html#E15:67"><i><font color="Green" title="E43">A8</font></i></a></i>;<br/>
<b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c10">G1</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c9">F1</font></span>)</span> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c15">f</font> = 
<span class="p1">(<span class="default"><a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <font color="Maroon" title="c5">G</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c13">b1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K3" title="FUNCTOR0:func.3">.</a> <font color="Maroon" title="c14">c1</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c16">f1</font></span>)</span>
<b>by </b><i><a class="txt" href="yellow20.html#E14:67"><i><font color="Green" title="E42">A7</font></i></a>, <a class="ref" href="functor3.html#T6" title="FUNCTOR3:th.6">FUNCTOR3:6</a></i>
<br/>.= 
<font color="Maroon" title="c5">G</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">F</font> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c16">f1</font></span>)</span>
<b>by </b><i><a class="txt" href="yellow20.html#E16:67"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="yellow20.html#E17:67"><i><font color="Green" title="E45">A10</font></i></a>, <a class="ref" href="functor0.html#D16" title="FUNCTOR0:def.16">FUNCTOR0:def 16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span> <a href="functor0.html#K6" title="FUNCTOR0:func.6">.</a> <font color="Maroon" title="c16">f1</font>
<b>by </b><i><a class="txt" href="yellow20.html#E16:67"><i><font color="Green" title="E44">A9</font></i></a>, <a class="ref" href="functor3.html#T6" title="FUNCTOR3:th.6">FUNCTOR3:6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K5" title="FUNCTOR0:func.5">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">G</font> <a href="functor3.html#K1" title="FUNCTOR3:func.1">*</a> <font color="Maroon" title="c4">F</font></span>)</span>,<font color="Maroon" title="c13">b1</font>,<font color="Maroon" title="c14">c1</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c16">f1</font>
<b>by </b><i><a class="txt" href="yellow20.html#E16:67"><i><font color="Green" title="E44">A9</font></i></a>, <a class="txt" href="yellow20.html#E17:67"><i><font color="Green" title="E45">A10</font></i></a>, <a class="ref" href="functor0.html#D16" title="FUNCTOR0:def.16">FUNCTOR0:def 16</a></i>
;<br/><br/>


</div>
