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<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#L2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon">B</font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V12">with_units</a>  <a href="altcat_1.html#L2">AltCatStr</a> , <font color="Maroon">C</font> be  non <a href="struct_0.html#V3">empty</a> <a href="altcat_1.html#V12">with_units</a>  <a href="altcat_1.html#L2">AltCatStr</a> ;<br/><b>let </b><font color="Maroon">F</font> be  <a href="functor0.html#V8">feasible</a> <a href="functor0.html#V11">Contravariant</a>  <a href="functor0.html#L2">FunctorStr</a> of <font color="Maroon">A</font>,<font color="Maroon">B</font>;<br/><b>let </b><font color="Maroon">G</font> be    <a href="functor0.html#L2">FunctorStr</a> of <font color="Maroon">B</font>,<font color="Maroon">C</font>;<br/><b>let </b><font color="Maroon">o</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>, <font color="Maroon">o1</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">A</font>;<br/>









<a NAME="E1:7"/><i><font color="Green">E31</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="functor0.html#U2">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">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="pboole.html#D3">PBOOLE:def 3</a></i>;<br/>
<a NAME="E2:7"/>
 <a href="funcop_1.html#K9">rng</a> the <a href="functor0.html#U1">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">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>
 
;<br/>
<b>then </b> <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">G</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font></span>)</span> = 
 <a href="relat_1.html#K1">dom</a> the <a href="functor0.html#U1">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">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_2.html#D1">FUNCT_2:def 1</a></i>
;<br/>
<a NAME="E4:7"/><b>then </b><i><font color="Green">E32</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o1</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">MorphMap</a> of <font color="Maroon">G</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">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="E5:7"/>
 <a href="relat_1.html#K1">dom</a> the <a href="functor0.html#U2">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">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="E6:7"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o1</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">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="E7:7"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o1</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">MorphMap</a> of <font color="Maroon">G</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">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">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="E8:7"/><b>then </b><i><font color="Green">E33</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o</font>,<font color="Maroon">o1</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">MorphMap</a> of <font color="Maroon">G</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font></span>)</span> <a href="altcat_2.html#K3">**</a> the <a href="functor0.html#U2">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">E34</font></i>: <span class="p1">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">G</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">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">o1</font></span><a href="tarski.html#K4">]</a></span> = 
the <a href="functor0.html#U2">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">ObjectMap</a> of <font color="Maroon">F</font> <a href="binop_1.html#K2">.</a> <font color="Maroon">o</font>,<font color="Maroon">o1</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">Morph-Map</a> <font color="Maroon">G</font>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3">.</a> <font color="Maroon">o1</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3">.</a> <font color="Maroon">o</font></span>)</span>
<b>by </b><i><a class="ref" href="functor0.html#T24">FUNCTOR0:24</a></i>
;<br/>
<b>thus </b> <a href="functor0.html#K4">Morph-Map</a> <span class="p1">(<span class="default"><font color="Maroon">G</font> <a href="functor0.html#K13">*</a> <font color="Maroon">F</font></span>)</span>,<font color="Maroon">o</font>,<font color="Maroon">o1</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">the <a href="functor0.html#U2">MorphMap</a> of <font color="Maroon">G</font> <a href="pboole.html#K7">*</a> the <a href="functor0.html#U1">ObjectMap</a> of <font color="Maroon">F</font></span>)</span> <a href="altcat_2.html#K3">**</a> the <a href="functor0.html#U2">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">o1</font>
<b>by </b><i><a class="ref" href="functor0.html#D37">FUNCTOR0:def 37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="functor0.html#K4">Morph-Map</a> <font color="Maroon">G</font>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3">.</a> <font color="Maroon">o1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">F</font> <a href="functor0.html#K3">.</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#K7">Morph-Map</a> <font color="Maroon">F</font>,<font color="Maroon">o</font>,<font color="Maroon">o1</font></span>)</span>
<b>by </b><i>, , <a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
;<br/>


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