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<b>set </b><font color="Maroon">OF</font> = the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font>;<br/>
<a NAME="E1:103_1_1"/>
<font color="Maroon">F</font> is <a href="functor0.html#V19" target="_self">injective</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E2:103_1_1"/><b>then </b>
<font color="Maroon">F</font> is <a href="functor0.html#V4" target="_self">one-to-one</a>
 
<b>by </b><i><a class="ref" href="functor0.html#T9" target="_self">Th9</a></i>;<br/>
<a NAME="E3:103_1_1"/><b>then </b><i><font color="Green">E23</font></i>: 
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="functor0.html#E3:103_1_1"><i><font color="Green">E23</font></i></a></i>;<br/>
<a NAME="E4:103_1_1"/>
<font color="Maroon">F</font> is <a href="functor0.html#V20" target="_self">surjective</a>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E5:103_1_1"/><b>then </b>
<font color="Maroon">F</font> is <a href="functor0.html#V5" target="_self">onto</a>
 
<b>by </b><i/>;<br/>
<a NAME="E6:103_1_1"/><b>then </b>
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i/>;<br/>
<a NAME="E7:103_1_1"/><b>then </b><i><font color="Green">E26</font></i>: 
 <a href="funcop_1.html#K9">rng</a> the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</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">B</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">OM</font> = the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="funct_1.html#K2">"</a>  as   <a href="functor0.html#NM1">bifunction</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">B</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A</font> <b>by </b><i>, <a class="ref" href="funct_2.html#T31">FUNCT_2:31</a></i>;<br/>
<b>reconsider </b><font color="Maroon">f</font> = the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">F</font> as    <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">B</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <b>by </b><i/>;<br/>
<span class="p1">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">B</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font></span>)</span> <a href="pboole.html#K7">*</a> <font color="Maroon">OM</font> = 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">B</font> <a href="pboole.html#K7">*</a> <span class="p1">(<span class="default">the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">OM</font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">B</font> <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">B</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">B</font></span><a href="zfmisc_1.html#K2">:]</a></span></span>)</span>
<b>by </b><i>, , <a class="ref" href="funct_2.html#T35">FUNCT_2:35</a></i>
<br/>.= 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">B</font>
<b>by </b><i/>
;<br/>
<a NAME="E11:103_1_1"/><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="pboole.html#K7">*</a> <font color="Maroon">OM</font> is    <a href="pboole.html#M3">ManySortedFunction</a> of the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">B</font>,the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <a href="pboole.html#K7">*</a> <font color="Maroon">OM</font>
 
<b>by </b><i><a class="ref" href="altcat_2.html#T5">ALTCAT_2:5</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">MM</font> = <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="msualg_3.html#K4">""</a> </span>)</span> <a href="pboole.html#K7">*</a> <font color="Maroon">OM</font> as    <a href="functor0.html#M1" target="_self">MSUnTrans</a> of <font color="Maroon">OM</font>,the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">B</font>,the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">A</font> <b>by </b><i/>;<br/>
<b>take </b><font color="Maroon">G</font> =  <a href="functor0.html#G2" target="_self">FunctorStr</a>(# <font color="Maroon">OM</font>,<font color="Maroon">MM</font> #);<br/>

<b>thus </b><a NAME="E13:103_1_1"/>
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">G</font> <a href="hidden.html#R1">=</a> the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="funct_1.html#K2">"</a> 
 ;<br/>

<b>take </b>
<font color="Maroon">f</font>
;<br/>

<b>thus </b><a NAME="E14:103_1_1"/>
( <font color="Maroon">f</font> <a href="pboole.html#R6">=</a> the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">F</font> &amp; the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">G</font> <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" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="funct_1.html#K2">"</a> </span>)</span> )
 ;<br/>


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