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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">x</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  implies  not <font color="Maroon" title="c1">x</font> is  <a href="facirc_1.html#V2" title="FACIRC_1:attr.2">with_pair</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:8_1_1"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<font color="Maroon" title="c1">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="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c1">x</font> is  <a href="facirc_1.html#V2" title="FACIRC_1:attr.2">with_pair</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="facirc_1.html#V1" title="FACIRC_1:attr.1">pair</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="facirc_1.html#D2" target="_self" title="FACIRC_1:def.2">FACIRC_1:def 2</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">x</font></span><br/>

<span class="kw">thus </span><a NAME="E2:8_1_1"/>
 not <font color="Maroon" title="c2">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:8_1_1"><span class="lab"><font color="Green" title="E3">A1</font></span></a></span>; <a class="txt" 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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