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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="vectsp_2.html#NM6">LeftMod</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:35"/><i><font color="Green">E11</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp; <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>4</sub></font> )
 ;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E2:35"/>
<font color="Maroon">c<sub>5</sub></font> is    <a href="lmod_7.html#M9" target="_self">Vector</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="lmod_7.html#M9" target="_self">Vector</a> of <font color="Maroon">c<sub>3</sub></font> ;<br/>
<a NAME="E4:35"/>
<font color="Maroon">c<sub>6</sub></font> is    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="lmod_7.html#E1:35"><i><font color="Green">E11</font></i></a>, <a class="ref" href="lmod_7.html#D11" target="_self">Def11</a></i>;<br/>
<a NAME="E5:35"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="txt" href="lmod_7.html#E1:35"><i><font color="Green">E11</font></i></a>, <a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:35"/>
<font color="Maroon">c<sub>5</sub></font> is    <a href="lmod_7.html#M9" target="_self">Vector</a> of <font color="Maroon">c<sub>4</sub></font>
 <b>by </b><i><a class="ref" href="lmod_7.html#D11" target="_self">Def11</a></i>;<br/>


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