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<b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>

<b>assume </b><a NAME="E1:9_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="ideal_1.html#V2" target="_self">left-ideal</a>
 ;<br/>

<a NAME="E2:9_1_1"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font> holds <br/><font color="Olive">b<sub>2</sub></font> <a href="group_1.html#K10">*</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="ideal_1.html#D2" target="_self">Def2</a></i>;<br/>
<b>hence </b><a NAME="E3:9_1_1"/>
<font color="Maroon">c<sub>2</sub></font> is <a href="ideal_1.html#V3" target="_self">right-ideal</a>
 <b>by </b><i><a class="ref" href="ideal_1.html#D3" target="_self">Def3</a></i>;<br/>


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