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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="funcsdom.html#NM1">Ring</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="classes2.html#NM1">Universe</a>;<br/>



<b>set </b><font color="Maroon">c<sub>3</sub></font> =  <a href="mod_2.html#K1">TrivialLMod</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<i><font color="Green">E10</font></i>:  <a href="vectsp_2.html#K8">op0</a>  = 
 <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
<br/>.= 
 <a href="algstr_1.html#K1">Extract</a> <a href="xboole_0.html#K1">{}</a> 
<b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>
;<br/>
<a NAME="E2:15"/><i><font color="Green">E11</font></i>: 
 <a href="mod_2.html#K1">TrivialLMod</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="vectsp_1.html#G4">VectSpStr</a>(# <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span>,<a href="midsp_1.html#K2">op2</a> ,<a href="vectsp_2.html#K8">op0</a> ,<span class="p1">(<span class="default"><a href="funct_3.html#K10">pr2</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span></span>)</span> #)
 
<b>by </b><i><a class="ref" href="mod_2.html#D2">MOD_2:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> =  <a href="rlvect_1.html#G1">LoopStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="mod_2.html#K1">TrivialLMod</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,the <a href="rlvect_1.html#U1">add</a> of <span class="p1">(<span class="default"><a href="mod_2.html#K1">TrivialLMod</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>,the <a href="struct_0.html#U2">Zero</a> of <span class="p1">(<span class="default"><a href="mod_2.html#K1">TrivialLMod</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> #) as    <a href="grcat_1.html#M2">Element</a> of  <a href="grcat_1.html#K19">GroupObjects</a> <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="modcat_1.html#E1:15"><i><font color="Green">E10</font></i></a>, <a class="ref" href="algstr_1.html#D4">ALGSTR_1:def 4</a>, <a class="ref" href="grcat_1.html#T42">GRCAT_1:42</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = the <a href="vectsp_1.html#U2">lmult</a> of <span class="p1">(<span class="default"><a href="mod_2.html#K1">TrivialLMod</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> as   <a href="funct_2.html#NM1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> <b>by </b><i><a class="txt" href="modcat_1.html#E2:15"><i><font color="Green">E11</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> <b>by </b><i><a class="ref" href="funct_2.html#T11">FUNCT_2:11</a></i>;<br/>
<b>take </b><font color="Maroon">c<sub>7</sub></font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="tarski.html#K4">]</a></span>;<br/>

<b>thus </b><a NAME="E6:15"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <span class="p2"><a href="tarski.html#K4">[</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font></span><a href="tarski.html#K4">]</a></span> where B is    <a href="grcat_1.html#M2">Element</a> of  <a href="grcat_1.html#K19">GroupObjects</a> <font color="Maroon">c<sub>2</sub></font>, B is    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p2"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span></span><a href="zfmisc_1.html#K2">:]</a></span>,<span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="xboole_0.html#K1">{}</a> </span><a href="tarski.html#K1">}</a></span> : verum </span>}</span> 
 ;<br/>

<b>thus </b><a NAME="E7:15"/>
 <a href="modcat_1.html#R1" target="_self">GO</a> <font color="Maroon">c<sub>7</sub></font>, <a href="mod_2.html#K1">TrivialLMod</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="modcat_1.html#D5" target="_self">Def5</a></i>;<br/>


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