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<a NAME="E1:15_1_1"/>
 ex <font color="Olive" title="b1">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <font color="Maroon" title="c1">S</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">[:</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">X</font> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span></span><a href="zfmisc_1.html#K3" title="ZFMISC_1:func.3">:]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="compos_1.html#D4" target="_self" title="COMPOS_1:def.4">Def17</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c2">II</font> =  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a>  the <a href="compos_1.html#U1" title="COMPOS_1:sel.1">Instructions</a> of <font color="Maroon" title="c1">S</font> as   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a> ;<br/>
<span class="kw">assume </span><a NAME="E3:15_1_1"/>
 <a href="compos_1.html#K4" title="COMPOS_1:func.4">InsCodes</a> <font color="Maroon" title="c1">S</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"> contradiction</span><br/>

<a NAME="E4:15_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">II</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<span class="kw">hence </span><a NAME="E5:15_1_1"/>
contradiction
 ; <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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