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<b>let </b><font color="Maroon">C1</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="altcat_1.html#L1">AltGraph</a> ;<br/><b>let </b><font color="Maroon">C2</font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_2.html#V1">reflexive</a>  <a href="altcat_1.html#L1">AltGraph</a> , <font color="Maroon">C3</font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_2.html#V1">reflexive</a>  <a href="altcat_1.html#L1">AltGraph</a> ;<br/><b>let </b><font color="Maroon">F</font> be  <a href="functor0.html#V6" target="_self">reflexive</a> <a href="functor0.html#V8" target="_self">feasible</a>  <a href="functor0.html#L2" target="_self">FunctorStr</a> of <font color="Maroon">C1</font>,<font color="Maroon">C2</font>;<br/><b>let </b><font color="Maroon">G</font> be    <a href="functor0.html#L2" target="_self">FunctorStr</a> of <font color="Maroon">C2</font>,<font color="Maroon">C3</font>;<br/><b>let </b><font color="Maroon">o</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C1</font>;<br/>









<a NAME="E1:100"/><i><font color="Green">E20</font></i>: 
 <a href="relat_1.html#K1">dom</a> 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"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C2</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="E2:100"/>
 <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="tarski.html#R1">c=</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">C2</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">C2</font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
;<br/>
<b>then </b> <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">G</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="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="relat_1.html#T46">RELAT_1:46</a></i>
<br/>.= 
<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="funct_2.html#D1">FUNCT_2:def 1</a></i>
;<br/>
<a NAME="E4:100"/><b>then </b><i><font color="Green">E23</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>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">G</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>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E5:100"/>
 <a href="relat_1.html#K1">dom</a> the <a href="functor0.html#U2" target="_self">MorphMap</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">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="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E6:100"/><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="relat_1.html#K1">dom</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="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E7:100"/><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> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default">the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">G</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></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">F</font></span>)</span>
 
<b>by </b><i>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E8:100"/><b>then </b><i><font color="Green">E26</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>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">G</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="altcat_2.html#K3">**</a> the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">F</font></span>)</span>
 
<b>by </b><i><a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>;<br/>
<i><font color="Green">E30</font></i>: <span class="p1">(<span class="default">the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">G</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="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">G</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#T22">FUNCT_1:22</a></i>
<br/>.= 
 <a href="functor0.html#K4" target="_self">Morph-Map</a> <font color="Maroon">G</font>,<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/>
<b>thus </b> <a href="functor0.html#K4" target="_self">Morph-Map</a> <span class="p1">(<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 class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">G</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="altcat_2.html#K3">**</a> the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">F</font></span>)</span> <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="functor0.html#T11" target="_self">Th11</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#NK3" target="_self">*</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="pboole.html#D24">PBOOLE:def 24</a></i>
;<br/>


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