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

<b>let </b><font color="Maroon">A</font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V2">transitive</a> <a href="altcat_1.html#V12">with_units</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/>

<b>set </b><font color="Maroon">CCA</font> = <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span>;<br/>
<a NAME="E1:21"/><i><font color="Green">E29</font></i>: 
the <a href="functor0.html#U1">ObjectMap</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="functor0.html#K15">"</a> </span>)</span> <a href="hidden.html#R1">=</a> the <a href="functor0.html#U1">ObjectMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K2">"</a> 
 
<b>by </b><i><a class="ref" href="functor0.html#D39">FUNCTOR0:def 39</a></i>;<br/>
<b>consider </b><font color="Maroon">f</font> being    <a href="pboole.html#M3">ManySortedFunction</a> of the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font>,the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span><b> such that </b><br/><a NAME="E3:21"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">f</font> <a href="pboole.html#R6">=</a> the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> &amp; the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="functor0.html#K15">"</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="msualg_3.html#K4">""</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default">the <a href="functor0.html#U1">ObjectMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K2">"</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="functor0.html#D39">FUNCTOR0:def 39</a></i>;<br/>
<i><font color="Green">E34</font></i>: the <a href="functor0.html#U1">ObjectMap</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="functor0.html#K15">"</a> </span>)</span> = 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="funct_1.html#K2">"</a> 
<b>by </b><i>, <a class="ref" href="functor0.html#D30">FUNCTOR0:def 30</a></i>
<br/>.= 
 <a href="partfun1.html#K6">id</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="ref" href="funct_1.html#T67">FUNCT_1:67</a></i>
<br/>.= 
the <a href="functor0.html#U1">ObjectMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#D30">FUNCTOR0:def 30</a></i>
;<br/>
<a NAME="E5:21"/><i><font color="Green">E35</font></i>: 
the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> is <a href="msualg_3.html#V1">"1-1"</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2"><b>proof </b></a><div class="add">

<a NAME="E1:21_2"/><i><font color="Green">E36</font></i>: 
the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="pboole.html#R6">=</a>  <a href="msualg_3.html#K2">id</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font>
 
<b>by </b><i><a class="ref" href="functor0.html#D30">FUNCTOR0:def 30</a></i>;<br/>
<a NAME="E2:21_2"/>
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span> holds <br/><span class="p1">(<span class="default"><a href="msualg_3.html#K2">id</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:21_2_1"/><i><font color="Green">E37</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>

<a NAME="E2:21_2_1"/>
 <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="funct_1.html#T52">FUNCT_1:52</a></i>;<br/>
<b>hence </b><a NAME="E3:21_2_1"/>
<span class="p1">(<span class="default"><a href="msualg_3.html#K2">id</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> is <a href="funct_1.html#V2">one-to-one</a>
 <b>by </b><i>, <a class="ref" href="msualg_3.html#D1">MSUALG_3:def 1</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:21_2"/>
the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> is <a href="msualg_3.html#V1">"1-1"</a>
 <b>by </b><i>, <a class="ref" href="msualg_3.html#T1">MSUALG_3:1</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E6:21"/><i><font color="Green">E38</font></i>: 
<font color="Maroon">f</font> is <a href="msualg_3.html#V2">"onto"</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_3"><b>proof </b></a><div class="add">

<a NAME="E1:21_3"/>
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span> holds <br/> <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_3_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:21_3_1"/><i><font color="Green">E43</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>

<a NAME="E2:21_3_1"/>
 <a href="relat_1.html#K1">dom</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E3:21_3_1"/><b>then </b><i><font color="Green">E44</font></i>: 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
;<br/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> = 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2">id</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, <a class="ref" href="functor0.html#D30">FUNCTOR0:def 30</a></i>
<br/>.= 
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="msualg_3.html#D1">MSUALG_3:def 1</a></i>
<br/>.= 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="pboole.html#K7">*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, , <a class="ref" href="funct_1.html#T38">FUNCT_1:38</a></i>
<br/>.= 
<span class="p1">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i><a class="ref" href="functor0.html#D30">FUNCTOR0:def 30</a></i>
;<br/>
<b>hence </b><a NAME="E5:21_3_1"/>
 <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:21_3"/>
<font color="Maroon">f</font> is <a href="msualg_3.html#V2">"onto"</a>
 <b>by </b><i><a class="ref" href="msualg_3.html#D3">MSUALG_3:def 3</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E7:21"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">f</font> <a href="msualg_3.html#K4">""</a>  <a href="pboole.html#R6">=</a> <font color="Maroon">f</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_4"><b>proof </b></a><div class="add">

<a NAME="E1:21_4"/>
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span> holds <br/><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="msualg_3.html#K4">""</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_4_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:21_4_1"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>

<b>then </b><span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="msualg_3.html#K4">""</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> = 
<span class="p1">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K2">"</a> 
<b>by </b><i>, , , <a class="ref" href="msualg_3.html#D5">MSUALG_3:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msualg_3.html#K2">id</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span> <a href="funct_1.html#K2">"</a> 
<b>by </b><i><a class="ref" href="functor0.html#D30">FUNCTOR0:def 30</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span></span>)</span> <a href="funct_1.html#K2">"</a> 
<b>by </b><i>, <a class="ref" href="msualg_3.html#D1">MSUALG_3:def 1</a></i>
<br/>.= 
 <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T67">FUNCT_1:67</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="msualg_3.html#K2">id</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="msualg_3.html#D1">MSUALG_3:def 1</a></i>
<br/>.= 
<font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
<b>by </b><i>, <a class="ref" href="functor0.html#D30">FUNCTOR0:def 30</a></i>
;<br/>
<b>hence </b><a NAME="E3:21_4_1"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="msualg_3.html#K4">""</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:21_4"/>
<font color="Maroon">f</font> <a href="msualg_3.html#K4">""</a>  <a href="pboole.html#R6">=</a> <font color="Maroon">f</font>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


</div><b>end;</b></div>
<a NAME="E8:21"/>
the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="pboole.html#K7">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="pboole.html#R6">=</a> the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_5"><b>proof </b></a><div class="add">

<a NAME="E1:21_5"/>
for <font color="Olive">i</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span> holds <br/><span class="p1">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="pboole.html#K7">*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="21_5_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">i</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:21_5_1"/><i><font color="Green">E49</font></i>: 
<font color="Maroon">i</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 ;<br/>

<a NAME="E2:21_5_1"/>
 <a href="relat_1.html#K1">dom</a> the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E3:21_5_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="functor0.html#U2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
;<br/>
<b>hence </b><a NAME="E4:21_5_1"/>
<span class="p1">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <span class="p2">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="pboole.html#K7">*</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p3"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font> <a href="hidden.html#R1">=</a> the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">i</font>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T38">FUNCT_1:38</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:21_5"/>
the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="pboole.html#K7">*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> <span class="p2"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span> <a href="pboole.html#R6">=</a> the <a href="functor0.html#U2">MorphMap</a> of <span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span>
 <b>by </b><i><a class="ref" href="pboole.html#T3">PBOOLE:3</a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E9:21"/>
<span class="p1">(<span class="default"><a href="functor0.html#K12">id</a> <font color="Maroon">A</font></span>)</span> <a href="functor0.html#K15">"</a>  <a href="hidden.html#R1">=</a>  <a href="functor0.html#K12">id</a> <font color="Maroon">A</font>
 <b>by </b><i>, , , , <a class="ref" href="functor0.html#D30">FUNCTOR0:def 30</a></i>;<br/>


</div>
