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<b>let </b><font color="Maroon" title="c1">UN</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>;<br/>

<b>set </b><font color="Maroon" title="c2">X</font> =  <a href="ringcat1.html#K10" title="RINGCAT1:func.10">Morphs</a> <span class="p1">(<span class="default"><a href="ringcat1.html#K9" title="RINGCAT1:func.9">RingObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span>;<br/>
<b>let </b><font color="Maroon" title="c3">f</font>, <font color="Maroon" title="c4">g</font> be   <a href="cat_1.html#NM2" title="CAT_1:NM.2">Morphism</a> of <span class="p1">(<span class="default"><a href="ringcat1.html#K18" title="RINGCAT1:func.18">RingCat</a> <font color="Maroon" title="c1">UN</font></span>)</span>;<br/>

<b>assume </b><a NAME="E1:75"/><i><font color="Green" title="E50">A1</font></i>: 
 <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c4">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c3">f</font>
 ;<br/>

<b>reconsider </b><font color="Maroon" title="c5">f'</font> = <font color="Maroon" title="c3">f</font> as  <a href="ringcat1.html#V2" title="RINGCAT1:attr.2">strict</a>  <a href="ringcat1.html#M3" title="RINGCAT1:mode.3">Element</a> of  <a href="ringcat1.html#K10" title="RINGCAT1:func.10">Morphs</a> <span class="p1">(<span class="default"><a href="ringcat1.html#K9" title="RINGCAT1:func.9">RingObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span> <b>by </b><i><a class="ref" href="ringcat1.html#T27" target="_self" title="RINGCAT1:th.27">Th27</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">g'</font> = <font color="Maroon" title="c4">g</font> as  <a href="ringcat1.html#V2" title="RINGCAT1:attr.2">strict</a>  <a href="ringcat1.html#M3" title="RINGCAT1:mode.3">Element</a> of  <a href="ringcat1.html#K10" title="RINGCAT1:func.10">Morphs</a> <span class="p1">(<span class="default"><a href="ringcat1.html#K9" title="RINGCAT1:func.9">RingObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span> <b>by </b><i><a class="ref" href="ringcat1.html#T27" target="_self" title="RINGCAT1:th.27">Th27</a></i>;<br/>
<a NAME="E4:75"/><i><font color="Green" title="E51">A2</font></i>: 
 <a href="ringcat1.html#K11" title="RINGCAT1:func.11">dom</a> <font color="Maroon" title="c6">g'</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#K12" title="RINGCAT1:func.12">cod</a> <font color="Maroon" title="c5">f'</font>
 
<b>by </b><i><a class="txt" href="ringcat1.html#E1:75"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="ringcat1.html#T30" target="_self" title="RINGCAT1:th.30">Th30</a></i>;<br/>
<a NAME="E5:75"/><b>then </b><i><font color="Green" title="E52">A3</font></i>: 
(  <a href="ringcat1.html#K1" title="RINGCAT1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g'</font> <a href="ringcat1.html#K6" title="RINGCAT1:func.6">*</a> <font color="Maroon" title="c5">f'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#K11" title="RINGCAT1:func.11">dom</a> <font color="Maroon" title="c5">f'</font> &amp;  <a href="ringcat1.html#K2" title="RINGCAT1:func.2">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">g'</font> <a href="ringcat1.html#K6" title="RINGCAT1:func.6">*</a> <font color="Maroon" title="c5">f'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="ringcat1.html#K12" title="RINGCAT1:func.12">cod</a> <font color="Maroon" title="c6">g'</font> )
 
<b>by </b><i><a class="ref" href="ringcat1.html#T11" target="_self" title="RINGCAT1:th.11">Th11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">gf</font> = <font color="Maroon" title="c6">g'</font> <a href="ringcat1.html#K6" title="RINGCAT1:func.6">*</a> <font color="Maroon" title="c5">f'</font> as    <a href="ringcat1.html#M3" title="RINGCAT1:mode.3">Element</a> of  <a href="ringcat1.html#K10" title="RINGCAT1:func.10">Morphs</a> <span class="p1">(<span class="default"><a href="ringcat1.html#K9" title="RINGCAT1:func.9">RingObjects</a> <font color="Maroon" title="c1">UN</font></span>)</span> <b>by </b><i><a class="txt" href="ringcat1.html#E4:75"><i><font color="Green" title="E51">A2</font></i></a>, <a class="ref" href="ringcat1.html#T25" target="_self" title="RINGCAT1:th.25">Th25</a></i>;<br/>
<a NAME="E7:75"/>
<font color="Maroon" title="c7">gf</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">g</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c3">f</font>
 
<b>by </b><i><a class="txt" href="ringcat1.html#E1:75"><i><font color="Green" title="E50">A1</font></i></a>, <a class="ref" href="ringcat1.html#T30" target="_self" title="RINGCAT1:th.30">Th30</a></i>;<br/>
<b>hence </b><a NAME="E8:75"/>
(  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K2" title="CAT_1:func.2">dom</a> <font color="Maroon" title="c3">f</font> &amp;  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">g</font> <a href="cat_1.html#K4" title="CAT_1:func.4">*</a> <font color="Maroon" title="c3">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="cat_1.html#K3" title="CAT_1:func.3">cod</a> <font color="Maroon" title="c4">g</font> )
 <b>by </b><i><a class="txt" href="ringcat1.html#E5:75"><i><font color="Green" title="E52">A3</font></i></a>, <a class="ref" href="ringcat1.html#T30" target="_self" title="RINGCAT1:th.30">Th30</a></i>;<br/>


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