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<span class="kw">let </span><font color="Maroon" title="c1">UN</font> be   <a href="classes2.html#NM1" title="CLASSES2:NM.1">Universe</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ringcat1.html#K9" title="RINGCAT1:func.9">RingObjects</a> <font color="Maroon" title="c1">UN</font> holds  <font color="Olive" title="b1">x</font> is   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="ringcat1.html#K9" title="RINGCAT1:func.9">RingObjects</a> <font color="Maroon" title="c1">UN</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">x</font> is   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a></span><br/>



<span class="kw">consider </span><font color="Maroon" title="c3">u</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <span class="kw"> such that </span><br/><a NAME="E2:59"/>
<font color="Maroon" title="c3">u</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">UN</font>
 <span class="kw">and </span><br/><a NAME="E3:59"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
 <a href="ringcat1.html#R2" title="RINGCAT1:pred.2">GO</a> <font color="Maroon" title="c3">u</font>,<font color="Maroon" title="c2">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ringcat1.html#D16" target="_self" onmouseover="rs('ringcat1/D16')" onmouseout="rh()">Def16</a></span>;<br/>
<a NAME="E4:59"/>
 ex <font color="Olive" title="b1">x1</font>, <font color="Olive" title="b2">x2</font>, <font color="Olive" title="b3">x3</font>, <font color="Olive" title="b4">x4</font>, <font color="Olive" title="b5">x5</font>, <font color="Olive" title="b6">x6</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  st <br/>( <font color="Maroon" title="c3">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">[</a><span class="default"><span class="p2"><a href="xtuple_0.html#K6" title="XTUPLE_0:func.6">[</a><span class="default"><font color="Olive" title="b1">x1</font>,<font color="Olive" title="b2">x2</font>,<font color="Olive" title="b3">x3</font>,<font color="Olive" title="b4">x4</font></span><a href="xtuple_0.html#K6" title="XTUPLE_0:func.6">]</a></span>,<font color="Olive" title="b5">x5</font>,<font color="Olive" title="b6">x6</font></span><a href="xtuple_0.html#K3" title="XTUPLE_0:func.3">]</a></span> &amp;  ex <font color="Olive" title="b7">G</font> being   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a> st <br/>( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b7">G</font> &amp; <font color="Olive" title="b1">x1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b7">G</font> &amp; <font color="Olive" title="b2">x2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="algstr_0.html#U1" title="ALGSTR_0:sel.1">addF</a> of <font color="Olive" title="b7">G</font> &amp; <font color="Olive" title="b3">x3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="vectsp_1.html#K4" title="VECTSP_1:func.4">comp</a> <font color="Olive" title="b7">G</font> &amp; <font color="Olive" title="b4">x4</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b7">G</font> &amp; <font color="Olive" title="b5">x5</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <font color="Olive" title="b7">G</font> &amp; <font color="Olive" title="b6">x6</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <font color="Olive" title="b7">G</font> ) )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:59"><span class="lab"><font color="Green" title="E33">A1</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:59"/>
<font color="Maroon" title="c2">x</font> is   <a href="algstr_0.html#V36" title="ALGSTR_0:attr.36">strict</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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