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<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">C1</font>, <font color="Maroon" title="c6">C2</font>, <font color="Maroon" title="c7">I1</font>, <font color="Maroon" title="c8">I2</font>, <font color="Maroon" title="c9">J1</font>, <font color="Maroon" title="c10">J2</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/>

<a NAME="E1:107"/>
(  <a href="aofa_000.html#K14" title="AOFA_000:func.14">if-then-else</a> <font color="Maroon" title="c5">C1</font>,<font color="Maroon" title="c7">I1</font>,<font color="Maroon" title="c8">I2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c5">C1</font>,<font color="Maroon" title="c7">I1</font>,<font color="Maroon" title="c8">I2</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> &amp;  <a href="aofa_000.html#K14" title="AOFA_000:func.14">if-then-else</a> <font color="Maroon" title="c6">C2</font>,<font color="Maroon" title="c9">J1</font>,<font color="Maroon" title="c10">J2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c6">C2</font>,<font color="Maroon" title="c9">J1</font>,<font color="Maroon" title="c10">J2</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="aofa_000.html#T63" target="_self" title="AOFA_000:th.63">Th63</a></i>;<br/>
<a NAME="E2:107"/><b>then </b>
(  <a href="aofa_000.html#K14" title="AOFA_000:func.14">if-then-else</a> <font color="Maroon" title="c5">C1</font>,<font color="Maroon" title="c7">I1</font>,<font color="Maroon" title="c8">I2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aofa_000.html#K14" title="AOFA_000:func.14">if-then-else</a> <font color="Maroon" title="c6">C2</font>,<font color="Maroon" title="c9">J1</font>,<font color="Maroon" title="c10">J2</font> implies <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c5">C1</font>,<font color="Maroon" title="c7">I1</font>,<font color="Maroon" title="c8">I2</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <span class="p1"><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">&lt;*</a><span class="default"><font color="Maroon" title="c6">C2</font>,<font color="Maroon" title="c9">J1</font>,<font color="Maroon" title="c10">J2</font></span><a href="finseq_4.html#K3" title="FINSEQ_4:func.3">*&gt;</a></span> )
 
<b>by </b><i><a class="ref" href="trees_4.html#T15" title="TREES_4:th.15">TREES_4:15</a></i>;<br/>
<b>hence </b><a NAME="E3:107"/>
(  <a href="aofa_000.html#K14" title="AOFA_000:func.14">if-then-else</a> <font color="Maroon" title="c5">C1</font>,<font color="Maroon" title="c7">I1</font>,<font color="Maroon" title="c8">I2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="aofa_000.html#K14" title="AOFA_000:func.14">if-then-else</a> <font color="Maroon" title="c6">C2</font>,<font color="Maroon" title="c9">J1</font>,<font color="Maroon" title="c10">J2</font> implies ( <font color="Maroon" title="c5">C1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">C2</font> &amp; <font color="Maroon" title="c7">I1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">J1</font> &amp; <font color="Maroon" title="c8">I2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">J2</font> ) )
 <b>by </b><i><a class="ref" href="group_7.html#T3" title="GROUP_7:th.3">GROUP_7:3</a></i>;<br/>


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