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<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:80_1_1_1"/>
<font color="Maroon">F</font> is <a href="functor0.html#V18" target="_self">full</a>
 ;<br/><b>then consider </b><font color="Maroon">B'</font> being    <a href="pboole.html#M1">ManySortedSet</a> of <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>, <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>,<font color="Maroon">B'</font><b> such that </b><br/><a NAME="E3:80_1_1_1"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">B'</font> <a href="pboole.html#R6">=</a> 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>and </b><br/><a NAME="E4:80_1_1_1"/><i><font color="Green">E23</font></i>: 
<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>
 <b>and </b><br/><a NAME="E5:80_1_1_1"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">f</font> is <a href="msualg_3.html#V2">"onto"</a>
 <b>by </b><i><a class="ref" href="functor0.html#T7" target="_self">Th7</a></i>;<br/><b>reconsider </b><font color="Maroon">f</font> = <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><a class="ref" href="functor0.html#T8" target="_self">Th8</a></i>;<br/><b>take </b><font color="Maroon">f</font> = <font color="Maroon">f</font>;<br/><b>thus </b><a NAME="E7:80_1_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>
 <b>by </b><i><a class="ref" href="functor0.html#T9" target="_self">Th9</a></i>;<br/><b>thus </b><a NAME="E8:80_1_1_1"/>
<font color="Maroon">f</font> is <a href="msualg_3.html#V2">"onto"</a>
 <b>by </b><i><a class="ref" href="functor0.html#T8" target="_self">Th8</a>, </i>;<br/></div>
<b>end;</b></div>

<b>given </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">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> such that </b><a NAME="E2:80_1_1"/><i><font color="Green">E30</font></i>: 
( <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; <font color="Maroon">f</font> is <a href="msualg_3.html#V2">"onto"</a> )
 ;<br/>

<b>take </b>
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>
; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D32" target="_self">FUNCTOR0:def 32</a><br/>

<b>thus </b><a NAME="E3:80_1_1"/>
 ex <font color="Olive">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">B</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> st <br/>( 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> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">B</font> <a href="funct_1.html#NK3" target="_self">*</a> the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> &amp; <font color="Olive">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; <font color="Olive">f</font> is <a href="msualg_3.html#V2">"onto"</a> )
 <b>by </b><i><a class="ref" href="functor0.html#T8" target="_self">Th8</a></i>;<br/>


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