<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="freealg.html#V1" title="FREEALG:attr.1">disjoint_with_NAT</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>set </b><font color="Maroon" title="c2">S</font> =  <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ;<br/>
<b>set </b><font color="Maroon" title="c3">G</font> =  <a href="freealg.html#K3" title="FREEALG:func.3">DTConUA</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<font color="Maroon" title="c1">X</font>;<br/>
<b>set </b><font color="Maroon" title="c4">A</font> =  <a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<font color="Maroon" title="c1">X</font>;<br/>
<b>let </b><font color="Maroon" title="c5">I1</font>, <font color="Maroon" title="c6">I2</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="freealg.html#K7" title="FREEALG:func.7">FreeUnivAlgNSG</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<font color="Maroon" title="c1">X</font></span>)</span>;<br/>

<b>set </b><font color="Maroon" title="c7">p</font> = <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c5">I1</font>,<font color="Maroon" title="c6">I2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>;<br/>
<a NAME="E1:103"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c5">I1</font>,<font color="Maroon" title="c6">I2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="trees_3.html#K5" title="TREES_3:func.5">FinTrees</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="freealg.html#K3" title="FREEALG:func.3">DTConUA</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<font color="Maroon" title="c1">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E2:103"/><b>then </b><i><font color="Green" title="E67">A1</font></i>: 
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c5">I1</font>,<font color="Maroon" title="c6">I2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> is    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="trees_3.html#K5" title="TREES_3:func.5">FinTrees</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="freealg.html#K3" title="FREEALG:func.3">DTConUA</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<font color="Maroon" title="c1">X</font></span>)</span>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4" title="FINSEQ_1:def.4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E3:103"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c5">I1</font>,<font color="Maroon" title="c6">I2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c5">I1</font>,<font color="Maroon" title="c6">I2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span>
 
<b>by </b><i><a class="ref" href="finseq_2.html#T147" title="FINSEQ_2:th.147">FINSEQ_2:147</a></i>;<br/>
<a NAME="E4:103"/><b>then </b><i><font color="Green" title="E68">A2</font></i>: 
( <font color="Maroon" title="c5">I1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c5">I1</font>,<font color="Maroon" title="c6">I2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> &amp; <font color="Maroon" title="c6">I2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c5">I1</font>,<font color="Maroon" title="c6">I2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/>
<font color="Maroon" title="c5">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c6">I2</font> = 
2 <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> <font color="Maroon" title="c5">I1</font>,<font color="Maroon" title="c6">I2</font>
<b>by </b><i><a class="ref" href="aofa_000.html#T59" target="_self" title="AOFA_000:th.59">Th59</a></i>
<br/>.= 
2 <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c5">I1</font>,<font color="Maroon" title="c6">I2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>

;<br/>
<b>hence </b><a NAME="E6:103"/>
( <font color="Maroon" title="c5">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c6">I2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c5">I1</font> &amp; <font color="Maroon" title="c5">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c6">I2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c6">I2</font> )
 <b>by </b><i><a class="txt" href="aofa_000.html#E2:103"><i><font color="Green" title="E67">A1</font></i></a>, <a class="txt" href="aofa_000.html#E4:103"><i><font color="Green" title="E68">A2</font></i></a>, <a class="ref" href="aofa_000.html#T3" target="_self" title="AOFA_000:th.3">Th3</a></i>;<br/>


</div>
