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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="classes2.html#NM1">Universe</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="ringcat1.html#K9" target="_self">RingObjects</a> <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>consider </b><font color="Maroon">c<sub>3</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E2:58"/><i><font color="Green">E37</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="ringcat1.html#R2" target="_self">GO</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> )
 <b>by </b><i><a class="ref" href="ringcat1.html#D17" target="_self">Def17</a></i>;<br/>
<a NAME="E3:58"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font>, <font color="Olive">b<sub>6</sub></font> being   <a href="hidden.html#M1">set</a>  st <br/>( <font color="Maroon">c<sub>3</sub></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">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font>,<font color="Olive">b<sub>4</sub></font></span><a href="mcart_1.html#K4">]</a></span>,<font color="Olive">b<sub>5</sub></font>,<font color="Olive">b<sub>6</sub></font></span><a href="mcart_1.html#K3">]</a></span> &amp; ex <font color="Olive">b<sub>7</sub></font> being <a href="vectsp_1.html#V3">strict</a> <a href="funcsdom.html#NM1">Ring</a> st <br/>( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>7</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>7</sub></font> &amp; <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Olive">b<sub>7</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#K7">comp</a> <font color="Olive">b<sub>7</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U2">Zero</a> of <font color="Olive">b<sub>7</sub></font> &amp; <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="group_1.html#U1">mult</a> of <font color="Olive">b<sub>7</sub></font> &amp; <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1">=</a> the <a href="vectsp_1.html#U1">unity</a> of <font color="Olive">b<sub>7</sub></font> ) )
 
<b>by </b><i><a class="txt" href="ringcat1.html#E2:58"><i><font color="Green">E37</font></i></a>, <a class="ref" href="ringcat1.html#D16" target="_self">Def16</a></i>;<br/>
<b>hence </b><a NAME="E4:58"/>
<font color="Maroon">c<sub>2</sub></font> is  <a href="vectsp_1.html#V3">strict</a> <a href="funcsdom.html#NM1">Ring</a>
 ;<br/>


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