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<b>consider </b><font color="Maroon" title="c3">o</font> being   <a href="altcat_1.html#NM1" title="ALTCAT_1:NM.1">object</a> of <font color="Maroon" title="c2">B</font>;<br/>
<b>set </b><font color="Maroon" title="c4">I</font> = <font color="Maroon" title="c1">A</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o</font></span>)</span>;<br/>
<a NAME="E2:4_1_1"/>
<font color="Maroon" title="c1">A</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o</font></span>)</span> is    <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_1"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:4_1_1_1"/>
( <font color="Maroon" title="c1">A</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o</font></span>)</span> is <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a> &amp; <font color="Maroon" title="c1">A</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o</font></span>)</span> is <a href="functor0.html#V12" title="FUNCTOR0:attr.12">id-preserving</a> &amp; ( ( <font color="Maroon" title="c1">A</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o</font></span>)</span> is <a href="functor0.html#V10" title="FUNCTOR0:attr.10">Covariant</a> &amp; <font color="Maroon" title="c1">A</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o</font></span>)</span> is <a href="functor0.html#V13" title="FUNCTOR0:attr.13">comp-preserving</a> ) or ( <font color="Maroon" title="c1">A</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o</font></span>)</span> is <a href="functor0.html#V11" title="FUNCTOR0:attr.11">Contravariant</a> &amp; <font color="Maroon" title="c1">A</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o</font></span>)</span> is <a href="functor0.html#V14" title="FUNCTOR0:attr.14">comp-reversing</a> ) ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D26" title="FUNCTOR0:def.26">FUNCTOR0:def 26</a><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c5">I</font> = <font color="Maroon" title="c1">A</font> <a href="functor0.html#K9" title="FUNCTOR0:func.9">--&gt;</a> <span class="p1">(<span class="default"><a href="altcat_1.html#K8" title="ALTCAT_1:func.8">idm</a> <font color="Maroon" title="c3">o</font></span>)</span> as    <a href="functor0.html#M2" title="FUNCTOR0:mode.2">Functor</a> of <font color="Maroon" title="c1">A</font>,<font color="Maroon" title="c2">B</font> ;<br/>
<b>take </b>
<font color="Maroon" title="c5">I</font>
;<br/>

<b>thus </b><a NAME="E4:4_1_1"/>
( <font color="Maroon" title="c5">I</font> is <a href="functor0.html#V9" title="FUNCTOR0:attr.9">strict</a> &amp; <font color="Maroon" title="c5">I</font> is <a href="functor0.html#V8" title="FUNCTOR0:attr.8">feasible</a> )
 ;<br/>

<b>thus </b><a NAME="E5:4_1_1"/>
<font color="Maroon" title="c5">I</font> is <a href="functor0.html#V15" title="FUNCTOR0:attr.15">covariant</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_2"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:4_1_1_2"/>
( <font color="Maroon" title="c5">I</font> is <a href="functor0.html#V10" title="FUNCTOR0:attr.10">Covariant</a> &amp; <font color="Maroon" title="c5">I</font> is <a href="functor0.html#V13" title="FUNCTOR0:attr.13">comp-preserving</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D27" title="FUNCTOR0:def.27">FUNCTOR0:def 27</a><br/>


</div><b>end;</b></div>

<b>thus </b><a NAME="E6:4_1_1"/>
<font color="Maroon" title="c5">I</font> is <a href="functor0.html#V16" title="FUNCTOR0:attr.16">contravariant</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="4_1_1_3"><b>proof </b></a><div class="add">

<b>thus </b><a NAME="E1:4_1_1_3"/>
( <font color="Maroon" title="c5">I</font> is <a href="functor0.html#V11" title="FUNCTOR0:attr.11">Contravariant</a> &amp; <font color="Maroon" title="c5">I</font> is <a href="functor0.html#V14" title="FUNCTOR0:attr.14">comp-reversing</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="functor0.html#D28" title="FUNCTOR0:def.28">FUNCTOR0:def 28</a><br/>


</div><b>end;</b></div>


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