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<span class="kw">let </span><font color="Maroon" title="c1">r</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">r</font> is  <a href="msafree5.html#V5" title="MSAFREE5:attr.5">non-trivial</a>  implies <font color="Maroon" title="c1">r</font> is  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:18_1_1"/>
 for <font color="Olive" title="b1">I</font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>   st <font color="Olive" title="b1">I</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <font color="Maroon" title="c1">r</font> holds <br/> not <font color="Olive" title="b1">I</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="msafree5.html#D7" target="_self" onmouseover="rs('msafree5/D7')" onmouseout="rh()">MSAFREE5:def 7</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">r</font> is  <a href="relat_1.html#V2" title="RELAT_1:attr.2">non-empty</a> </span><br/>

<span class="kw">hence </span><a NAME="E2:18_1_1"/>
 not  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">rng</a> <font color="Maroon" title="c1">r</font>
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="relat_1.html#D9" onmouseover="rs('relat_1/D9')" onmouseout="rh()">RELAT_1:def 9</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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