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<b>let </b><font color="Maroon" title="c2">I</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font>;<br/>

<b>assume </b><a NAME="E1:9_1_1"/>
<font color="Maroon" title="c2">I</font> is <a href="ideal_1.html#V2" title="IDEAL_1:attr.2">left-ideal</a>
 ;<br/>

<a NAME="E2:9_1_1"/><b>then </b>
for <font color="Olive" title="b1">p</font>, <font color="Olive" title="b2">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b2">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">I</font> holds <br/><font color="Olive" title="b2">x</font> <a href="group_1.html#K9" title="GROUP_1:func.9">*</a> <font color="Olive" title="b1">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">I</font>
 
<b>by </b><i><a class="ref" href="ideal_1.html#D2" target="_self" title="IDEAL_1:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E3:9_1_1"/>
<font color="Maroon" title="c2">I</font> is <a href="ideal_1.html#V3" title="IDEAL_1:attr.3">right-ideal</a>
 <b>by </b><i><a class="ref" href="ideal_1.html#D3" target="_self" title="IDEAL_1:def.3">Def3</a></i>;<br/>


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