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<b>let </b><font color="Maroon">o</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C1</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D21" target="_self">FUNCTOR0:def 21</a><br/>

<a NAME="E1:101_1_1"/><i><font color="Green">E20</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="tarski.html#K4">]</a></span> <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">C1</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C1</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E2:101_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</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="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>then </b><span class="p1">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C2</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="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="tarski.html#K4">]</a></span> = 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C2</font> <a href="funct_1.html#K1">.</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="binop_1.html#K2">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font></span>)</span>
<b>by </b><i><a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C2</font> <a href="binop_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span>
<b>by </b><i><a class="ref" href="altcat_1.html#D2">ALTCAT_1:def 2</a></i>
;<br/>
<a NAME="E4:101_1_1"/><b>then </b><i><font color="Green">E23</font></i>: 
<span class="p1">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C2</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="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 
<b>by </b><i><a class="ref" href="altcat_2.html#D7">ALTCAT_2:def 7</a></i>;<br/>
<a NAME="E5:101_1_1"/>
the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">F</font> is    <a href="pboole.html#M3">ManySortedFunction</a> of the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C1</font>,the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C2</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/>
<a NAME="E6:101_1_1"/><b>then </b>
 <a href="functor0.html#K4" target="_self">Morph-Map</a> <font color="Maroon">F</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font> is   <a href="funct_2.html#NM1">Function</a> of the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C1</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="tarski.html#K4">]</a></span>,<span class="p1">(<span class="default">the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C2</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="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i>, <a class="ref" href="pboole.html#D18">PBOOLE:def 18</a></i>;<br/>
<b>then </b> <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" target="_self">Morph-Map</a> <font color="Maroon">F</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span>)</span> = 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C1</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font>
<b>by </b><i>, <a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
<br/>.= 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o</font></span><a href="altcat_1.html#K1">^&gt;</a></span>
<b>by </b><i><a class="ref" href="altcat_1.html#D2">ALTCAT_1:def 2</a></i>
;<br/>
<a NAME="E8:101_1_1"/><b>then </b><i><font color="Green">E26</font></i>: 
 <a href="altcat_1.html#K8">idm</a> <font color="Maroon">o</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K4" target="_self">Morph-Map</a> <font color="Maroon">F</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span>)</span>
 
<b>by </b><i><a class="ref" href="altcat_1.html#T23">ALTCAT_1:23</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="functor0.html#K4" target="_self">Morph-Map</a> <span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="functor0.html#K13" target="_self">*</a> <font color="Maroon">F</font></span>)</span>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">o</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor0.html#K4" target="_self">Morph-Map</a> <font color="Maroon">G</font>,<span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span>,<span class="p3">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><a href="functor0.html#K4" target="_self">Morph-Map</a> <font color="Maroon">F</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">o</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K4" target="_self">Morph-Map</a> <font color="Maroon">G</font>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="functor0.html#K4" target="_self">Morph-Map</a> <font color="Maroon">F</font>,<font color="Maroon">o</font>,<font color="Maroon">o</font></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><a href="altcat_1.html#K8">idm</a> <font color="Maroon">o</font></span>)</span></span>)</span>
<b>by </b><i>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K4" target="_self">Morph-Map</a> <font color="Maroon">G</font>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8">idm</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#T3" target="_self">Th3</a></i>
<br/>.= 
 <a href="altcat_1.html#K8">idm</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="functor0.html#K3" target="_self">.</a> <span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#T3" target="_self">Th3</a></i>
<br/>.= 
 <a href="altcat_1.html#K8">idm</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">G</font> <a href="functor0.html#K13" target="_self">*</a> <font color="Maroon">F</font></span>)</span> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o</font></span>)</span>
<b>by </b><i/>
;<br/>


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