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<b>let </b><font color="Maroon">UN</font> be   <a href="classes2.html#NM1">Universe</a>;<br/>

<b>set </b><font color="Maroon">C</font> =  <a href="ringcat1.html#K18" target="_self">RingCat</a> <font color="Maroon">UN</font>;<br/>
<b>set </b><font color="Maroon">V</font> =  <a href="ringcat1.html#K9" target="_self">RingObjects</a> <font color="Maroon">UN</font>;<br/>
<b>set </b><font color="Maroon">X</font> =  <a href="ringcat1.html#K10" target="_self">Morphs</a> <span class="p1">(<span class="default"><a href="ringcat1.html#K9" target="_self">RingObjects</a> <font color="Maroon">UN</font></span>)</span>;<br/>
<b>let </b><font color="Maroon">f</font> be   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="ringcat1.html#K18" target="_self">RingCat</a> <font color="Maroon">UN</font></span>)</span>;<br/><b>let </b><font color="Maroon">f'</font> be    <a href="ringcat1.html#M3" target="_self">Element</a> of  <a href="ringcat1.html#K10" target="_self">Morphs</a> <span class="p1">(<span class="default"><a href="ringcat1.html#K9" target="_self">RingObjects</a> <font color="Maroon">UN</font></span>)</span>;<br/><b>let </b><font color="Maroon">b</font> be   <a href="cat_1.html#NM1">Object</a> of <span class="p1">(<span class="default"><a href="ringcat1.html#K18" target="_self">RingCat</a> <font color="Maroon">UN</font></span>)</span>;<br/><b>let </b><font color="Maroon">b'</font> be    <a href="ringcat1.html#M2" target="_self">Element</a> of  <a href="ringcat1.html#K9" target="_self">RingObjects</a> <font color="Maroon">UN</font>;<br/>







<a NAME="E1:70"/>
 ex <font color="Olive">G</font>, <font color="Olive">H</font> being   <a href="ringcat1.html#M2" target="_self">Element</a> of  <a href="ringcat1.html#K9" target="_self">RingObjects</a> <font color="Maroon">UN</font> st <br/>( <font color="Olive">G</font> <a href="ringcat1.html#R1" target="_self">&lt;=</a> <font color="Olive">H</font> &amp; <font color="Maroon">f</font> is    <a href="ringcat1.html#M1" target="_self">Morphism</a> of <font color="Olive">G</font>,<font color="Olive">H</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E2:70"/>
<font color="Maroon">f</font> is  <a href="ringcat1.html#V2" target="_self">strict</a>  <a href="ringcat1.html#M3" target="_self">Element</a> of  <a href="ringcat1.html#K10" target="_self">Morphs</a> <span class="p1">(<span class="default"><a href="ringcat1.html#K9" target="_self">RingObjects</a> <font color="Maroon">UN</font></span>)</span>
 ;<br/>

<b>thus </b><a NAME="E3:70"/>
<font color="Maroon">f'</font> is   <a href="cat_1.html#NM2">Morphism</a> of <span class="p1">(<span class="default"><a href="ringcat1.html#K18" target="_self">RingCat</a> <font color="Maroon">UN</font></span>)</span>
 ;<br/>

<b>consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E5:70"/><i><font color="Green">E31</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">UN</font> &amp;  <a href="ringcat1.html#R2" target="_self">GO</a> <font color="Maroon">x</font>,<font color="Maroon">b</font> )
 <b>by </b><i/>;<br/>
<a NAME="E6:70"/>
 ex <font color="Olive">x1</font>, <font color="Olive">x2</font>, <font color="Olive">x3</font>, <font color="Olive">x4</font>, <font color="Olive">x5</font>, <font color="Olive">x6</font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="mcart_1.html#K3">[</a><span class="default"><span class="p2"><a href="mcart_1.html#K4">[</a><span class="default"><font color="Olive">x1</font>,<font color="Olive">x2</font>,<font color="Olive">x3</font>,<font color="Olive">x4</font></span><a href="mcart_1.html#K4">]</a></span>,<font color="Olive">x5</font>,<font color="Olive">x6</font></span><a href="mcart_1.html#K3">]</a></span> &amp;  ex <font color="Olive">G</font> being <a href="vectsp_1.html#V3">strict</a> <a href="funcsdom.html#NM1">Ring</a> st <br/>( <font color="Maroon">b</font> <a href="hidden.html#R1">=</a> <font color="Olive">G</font> &amp; <font color="Olive">x1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">G</font> &amp; <font color="Olive">x2</font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Olive">G</font> &amp; <font color="Olive">x3</font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#K7">comp</a> <font color="Olive">G</font> &amp; <font color="Olive">x4</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <font color="Olive">G</font> &amp; <font color="Olive">x5</font> <a href="hidden.html#R1">=</a> the <a href="group_1.html#U1">mult</a> of <font color="Olive">G</font> &amp; <font color="Olive">x6</font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U1">unity</a> of <font color="Olive">G</font> ) )
 
<b>by </b><i><a class="ref" href="ringcat1.html#D9" target="_self">Def9</a>, <a class="txt" href="ringcat1.html#E5:70"><i><font color="Green">E31</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:70"/>
<font color="Maroon">b</font> is  <a href="vectsp_1.html#V3">strict</a>  <a href="ringcat1.html#M2" target="_self">Element</a> of  <a href="ringcat1.html#K9" target="_self">RingObjects</a> <font color="Maroon">UN</font>
 ;<br/>

<b>thus </b><a NAME="E8:70"/>
<font color="Maroon">b'</font> is   <a href="cat_1.html#NM1">Object</a> of <span class="p1">(<span class="default"><a href="ringcat1.html#K18" target="_self">RingCat</a> <font color="Maroon">UN</font></span>)</span>
 ;<br/>


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