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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="compos_0.html#V1" title="COMPOS_0:attr.1">standard-ins</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">  for <font color="Olive" title="b1">I</font>, <font color="Olive" title="b2">J</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>  st  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Olive" title="b2">J</font> &amp;  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Olive" title="b2">J</font> &amp;  <a href="compos_0.html#K3" title="COMPOS_0:func.3">AddressPart</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K3" title="COMPOS_0:func.3">AddressPart</a> <font color="Olive" title="b2">J</font> holds <br/><font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">J</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font>, <font color="Maroon" title="c3">J</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font>; <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"> (  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c3">J</font> &amp;  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c3">J</font> &amp;  <a href="compos_0.html#K3" title="COMPOS_0:func.3">AddressPart</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K3" title="COMPOS_0:func.3">AddressPart</a> <font color="Maroon" title="c3">J</font> implies <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">J</font> )</span><br/>



<span class="kw">consider </span><font color="Maroon" title="c4">X</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <span class="kw"> such that </span><br/><a NAME="E2:24"/><span class="lab"><font color="Green" title="E8">A1</font></span>: 
<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#NK1" title="NUMBERS:NK.1">NAT</a>,<span class="p2">(<span class="default"><a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> <a href="finseq_1.html#K13" title="FINSEQ_1:func.13">*</a></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c4">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_0.html#D1" target="_self" onmouseover="rs('compos_0/D1')" onmouseout="rh()">Def1</a></span>;<br/>
<a NAME="E3:24"/><span class="lab"><font color="Green" title="E9">A2</font></span>: 
<font color="Maroon" title="c2">I</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">S</font>
 
;<br/>
<a NAME="E4:24"/>
<font color="Maroon" title="c3">J</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Maroon" title="c1">S</font>
 
;<br/>
<span class="kw">hence </span><a NAME="E5:24"/>
(  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K5" title="COMPOS_0:func.5">InsCode</a> <font color="Maroon" title="c3">J</font> &amp;  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K2" title="COMPOS_0:func.2">JumpPart</a> <font color="Maroon" title="c3">J</font> &amp;  <a href="compos_0.html#K3" title="COMPOS_0:func.3">AddressPart</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="compos_0.html#K3" title="COMPOS_0:func.3">AddressPart</a> <font color="Maroon" title="c3">J</font> implies <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">J</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:24"><span class="lab"><font color="Green" title="E9">A2</font></span></a>, <a class="txt" href="#E2:24"><span class="lab"><font color="Green" title="E8">A1</font></span></a>, <a class="ref" href="recdef_2.html#T10" onmouseover="rs('recdef_2/T10')" onmouseout="rh()">RECDEF_2:10</a></span>; <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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