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<b>let </b><font color="Maroon" title="c1">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <a href="ideal_1.html#NM3" title="IDEAL_1:NM.3">LeftIdeal</a> of <font color="Maroon" title="c1">L</font> holds  <font color="Olive" title="b1">I</font> <a href="ideal_1.html#K8" title="IDEAL_1:func.8">-LeftIdeal</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">I</font></span><br/><b>let </b><font color="Maroon" title="c2">I</font> be   <a href="ideal_1.html#NM3" title="IDEAL_1:NM.3">LeftIdeal</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">I</font> <a href="ideal_1.html#K8" title="IDEAL_1:func.8">-LeftIdeal</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">I</font></span><br/>



<a NAME="E1:75"/>
( <font color="Maroon" title="c2">I</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">I</font> <a href="ideal_1.html#K8" title="IDEAL_1:func.8">-LeftIdeal</a>  &amp; <font color="Maroon" title="c2">I</font> <a href="ideal_1.html#K8" title="IDEAL_1:func.8">-LeftIdeal</a>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c2">I</font> )
 
<b>by </b><i><a class="ref" href="ideal_1.html#D16" target="_self" title="IDEAL_1:def.16">Def16</a></i>;<br/>
<b>hence </b><a NAME="E2:75"/>
<font color="Maroon" title="c2">I</font> <a href="ideal_1.html#K8" title="IDEAL_1:func.8">-LeftIdeal</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">I</font>
 <b>by </b><i><a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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