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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>   <a href="algstr_0.html#L4" title="ALGSTR_0:struct.4">multLoopStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">X</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font>  st <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="gcd_1.html#K3" title="GCD_1:func.3">Classes</a> <font color="Maroon" title="c1">R</font> holds <br/> not <font color="Olive" title="b1">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="gcd_1.html#K3" title="GCD_1:func.3">Classes</a> <font color="Maroon" title="c1">R</font> implies  not <font color="Maroon" title="c2">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:37"/>
<font color="Maroon" title="c2">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="gcd_1.html#K3" title="GCD_1:func.3">Classes</a> <font color="Maroon" title="c1">R</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c2">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> </span><br/>

<a NAME="E2:37"/><span class="kw">then </span>
 ex <font color="Olive" title="b1">a</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="Maroon" title="c2">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="gcd_1.html#K2" title="GCD_1:func.2">Class</a> <font color="Olive" title="b1">a</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="gcd_1.html#D6" target="_self" title="GCD_1:def.6">Def6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:37"/>
not <font color="Maroon" title="c2">X</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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