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<b>consider </b><font color="Maroon">I2'</font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">B'</font> being    <a href="pboole.html#M1">ManySortedSet</a> of <font color="Maroon">I2'</font>, <font color="Maroon">f'</font> being   <a href="funct_2.html#NM1">Function</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">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>,<font color="Maroon">I2'</font><b> such that </b><br/><a NAME="E2:44_1_1"/><i><font color="Green">E20</font></i>: 
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="funct_2.html#R1">=</a> <font color="Maroon">f'</font>
 <b>and </b><br/><a NAME="E3:44_1_1"/><i><font color="Green">E23</font></i>: 
the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">B'</font>
 <b>and </b><br/><a NAME="E4:44_1_1"/><i><font color="Green">E26</font></i>: 
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>,<font color="Maroon">B'</font> <a href="pboole.html#K7">*</a> <font color="Maroon">f'</font>
 <b>by </b><i/>;<br/>
<i><font color="Green">E30</font></i>: 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">o1</font>,<font color="Maroon">o2</font></span><a href="tarski.html#K4">]</a></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">o1</font>,<font color="Maroon">o2</font>

<br/>.= 
<span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o1</font>,<font color="Maroon">o2</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="E6:44_1_1"/><i><font color="Green">E31</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o1</font>,<font color="Maroon">o2</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="E7:44_1_1"/>
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> is <a href="functor0.html#V2" target="_self">Contravariant</a>
 
<b>by </b><i><a class="txt" href="functor0.html#E6:44_1_1"><i><font color="Green">E31</font></i></a></i>;<br/>
<b>then consider </b><font color="Maroon">g</font> being   <a href="funct_2.html#NM1">Function</a> of 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">C2</font><b> such that </b><br/><a NAME="E9:44_1_1"/><i><font color="Green">E33</font></i>: 
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <font color="Maroon">F</font> <a href="funct_2.html#R2">=</a>  <a href="functor0.html#K1" target="_self">~</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K16">:]</a></span>
 <b>by </b><i/>;<br/>
<a NAME="E10:44_1_1"/><i><font color="Green">E34</font></i>: 
 <a href="relset_1.html#K4">dom</a> <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="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E11:44_1_1"/><b>then </b>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o1</font>,<font color="Maroon">o1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K1" target="_self">~</a> <span class="p2"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K16">:]</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="functor0.html#E9:44_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="functor0.html#T1" target="_self">Th1</a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E12:44_1_1"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o1</font>,<font color="Maroon">o1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K16">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T43">FUNCT_4:43</a></i>;<br/>
<i><font color="Green">E37</font></i>: <font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o1</font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K16">:]</a></span> <a href="binop_1.html#K2">.</a> <font color="Maroon">o1</font>,<font color="Maroon">o1</font></span>)</span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="ref" href="functor0.html#T1" target="_self">Th1</a>, <a class="ref" href="functor0.html#T3" target="_self">Th3</a>, <a class="ref" href="funct_4.html#D2">FUNCT_4:def 2</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">o1</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">o1</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="ref" href="funct_3.html#T96">FUNCT_3:96</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">o1</font>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
;<br/>
<a NAME="E14:44_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o2</font>,<font color="Maroon">o2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K1" target="_self">~</a> <span class="p2"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K16">:]</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="functor0.html#E9:44_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="functor0.html#T1" target="_self">Th1</a>, , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E15:44_1_1"/><b>then </b><i><font color="Green">E45</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o2</font>,<font color="Maroon">o2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K16">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T43">FUNCT_4:43</a></i>;<br/>
<i><font color="Green">E46</font></i>: <font color="Maroon">F</font> <a href="functor0.html#K3" target="_self">.</a> <font color="Maroon">o2</font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K16">:]</a></span> <a href="binop_1.html#K2">.</a> <font color="Maroon">o2</font>,<font color="Maroon">o2</font></span>)</span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="ref" href="functor0.html#T1" target="_self">Th1</a>, , <a class="ref" href="funct_4.html#D2">FUNCT_4:def 2</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">o2</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">o2</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="mcart_1.html#K1">`1</a> 
<b>by </b><i><a class="ref" href="funct_3.html#T96">FUNCT_3:96</a></i>
<br/>.= 
<font color="Maroon">g</font> <a href="funct_2.html#K3">.</a> <font color="Maroon">o2</font>
<b>by </b><i><a class="ref" href="mcart_1.html#T7">MCART_1:7</a></i>
;<br/>
<a NAME="E17:44_1_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o1</font>,<font color="Maroon">o2</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="functor0.html#K1" target="_self">~</a> <span class="p2"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K16">:]</a></span></span>)</span>
 
<b>by </b><i><a class="txt" href="functor0.html#E9:44_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="functor0.html#T1" target="_self">Th1</a>, , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E18:44_1_1"/><b>then </b><i><font color="Green">E47</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o2</font>,<font color="Maroon">o1</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K4">dom</a> <span class="p1"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K16">:]</a></span>
 
<b>by </b><i><a class="ref" href="funct_4.html#T43">FUNCT_4:43</a></i>;<br/>
<i><font color="Green">E63</font></i>: <span class="p1">(<span class="default"><font color="Maroon">B'</font> <a href="pboole.html#K7">*</a> <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">o1</font>,<font color="Maroon">o2</font></span><a href="tarski.html#K4">]</a></span> = 
<font color="Maroon">B'</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Maroon">f'</font> <a href="funct_1.html#K1">.</a> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o1</font>,<font color="Maroon">o2</font></span><a href="tarski.html#K4">]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="functor0.html#E13:44_1_1"><i><font color="Green">E37</font></i></a>, , <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<font color="Maroon">B'</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><span class="p2"><a href="funct_3.html#K16">[:</a><span class="default"><font color="Maroon">g</font>,<font color="Maroon">g</font></span><a href="funct_3.html#K16">:]</a></span> <a href="binop_1.html#K2">.</a> <font color="Maroon">o2</font>,<font color="Maroon">o1</font></span>)</span>
<b>by </b><i><a class="txt" href="functor0.html#E9:44_1_1"><i><font color="Green">E33</font></i></a>, <a class="ref" href="functor0.html#T1" target="_self">Th1</a>, <a class="ref" href="functor0.html#T4" target="_self">Th4</a>, <a class="ref" href="funct_4.html#D2">FUNCT_4:def 2</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">o2</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">o1</font></span>)</span>
<b>by </b><i><a class="txt" href="functor0.html#E10:44_1_1"><i><font color="Green">E34</font></i></a>, , , <a class="ref" href="funct_3.html#T96">FUNCT_3:96</a></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">o2</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">o1</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="E20:44_1_1"/>
the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">F</font> <a href="funct_1.html#K1">.</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">o1</font>,<font color="Maroon">o2</font></span><a href="tarski.html#K4">]</a></span> 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">o1</font>,<font color="Maroon">o2</font></span><a href="tarski.html#K4">]</a></span>,<span class="p1">(<span class="default"><font color="Maroon">B'</font> <a href="pboole.html#K7">*</a> <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">o1</font>,<font color="Maroon">o2</font></span><a href="tarski.html#K4">]</a></span>
 
<b>by </b><i>, <a class="txt" href="functor0.html#E13:44_1_1"><i><font color="Green">E37</font></i></a>, <a class="ref" href="pboole.html#D18">PBOOLE:def 18</a></i>;<br/>
<a NAME="E21:44_1_1"/><b>then </b>
the <a href="functor0.html#U2" target="_self">MorphMap</a> of <font color="Maroon">F</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">o1</font>,<font color="Maroon">o2</font> is   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o1</font>,<font color="Maroon">o2</font></span><a href="altcat_1.html#K1">^&gt;</a></span>,<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">o2</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">o1</font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span>
 
<b>by </b><i><a class="txt" href="functor0.html#E12:44_1_1"><i><font color="Green">E36</font></i></a>, <a class="txt" href="functor0.html#E15:44_1_1"><i><font color="Green">E45</font></i></a></i>;<br/>
<b>hence </b><a NAME="E22:44_1_1"/>
 <a href="functor0.html#K4" target="_self">Morph-Map</a> <font color="Maroon">F</font>,<font color="Maroon">o1</font>,<font color="Maroon">o2</font> is   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="altcat_1.html#K1">&lt;^</a><span class="default"><font color="Maroon">o1</font>,<font color="Maroon">o2</font></span><a href="altcat_1.html#K1">^&gt;</a></span>,<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">o2</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">o1</font></span>)</span></span><a href="altcat_1.html#K1">^&gt;</a></span>
 ;<br/>


</div>
