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<a NAME="E1:48_1_1"/>
<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> <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="E2:48_1_1"/><b>then </b><i><font color="Green">E20</font></i>: 
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon">C1</font> <a href="functor0.html#K9" target="_self">--&gt;</a> <font color="Maroon">m</font></span>)</span> <a href="funct_2.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> <a href="pboole.html#K9">--&gt;</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/>;<br/>
<b>hence </b><a NAME="E3:48_1_1"/>
( the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon">C1</font> <a href="functor0.html#K9" target="_self">--&gt;</a> <font color="Maroon">m</font></span>)</span> is <a href="functor0.html#V1" target="_self">Covariant</a> &amp; the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon">C1</font> <a href="functor0.html#K9" target="_self">--&gt;</a> <font color="Maroon">m</font></span>)</span> is <a href="functor0.html#V2" target="_self">Contravariant</a> )
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D13" target="_self">FUNCTOR0:def 13</a>,<a class="ref" href="functor0.html#D14" target="_self">FUNCTOR0:def 14</a><br/>

<b>let </b><font color="Maroon">o1</font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">C1</font>, <font color="Maroon">o2</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#D12" target="_self">FUNCTOR0:def 12</a><br/>

<b>assume </b><a NAME="E4:48_1_1"/>
<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> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/>

<a NAME="E5:48_1_1"/><i><font color="Green">E23</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="E6:48_1_1"/>
the <a href="functor0.html#U1" target="_self">ObjectMap</a> of <span class="p1">(<span class="default"><font color="Maroon">C1</font> <a href="functor0.html#K9" target="_self">--&gt;</a> <font color="Maroon">m</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">o1</font>,<font color="Maroon">o2</font> <a href="hidden.html#R1">=</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="funcop_1.html#T13">FUNCOP_1:13</a></i>;<br/>
<a NAME="E7:48_1_1"/><b>then </b>
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 <span class="p2">(<span class="default"><font color="Maroon">C1</font> <a href="functor0.html#K9" target="_self">--&gt;</a> <font color="Maroon">m</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">o1</font>,<font color="Maroon">o2</font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="altcat_1.html#U1">Arrows</a> of <font color="Maroon">C2</font> <a href="binop_1.html#K1">.</a> <font color="Maroon">o</font>,<font color="Maroon">o</font>
 
;<br/>
<b>hence </b><a NAME="E8:48_1_1"/>
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 <span class="p2">(<span class="default"><font color="Maroon">C1</font> <a href="functor0.html#K9" target="_self">--&gt;</a> <font color="Maroon">m</font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">o1</font>,<font color="Maroon">o2</font></span>)</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#D6">ALTCAT_2:def 6</a></i>;<br/>


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