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

<span class="kw">set </span><font color="Maroon" title="c2">S</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/>
<span class="kw">set </span><font color="Maroon" title="c3">char</font> =  <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ;<br/>
<a NAME="E1:97_1_1"/><span class="lab"><font color="Green" title="E61">A1</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,2</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> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E2:97_1_1"/><span class="lab"><font color="Green" title="E62">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default">3,2</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> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E3:97_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E63">A3</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="finseq_1.html#T22" title="FINSEQ_1:th.22">FINSEQ_1:22</a></span>;<br/>
<a NAME="E4:97_1_1"/><span class="lab"><font color="Green" title="E64">A4</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="freealg.html#D11" title="FREEALG:def.11">FREEALG:def 11</a></span>;<br/>
<a NAME="E5:97_1_1"/><span class="lab"><font color="Green" title="E65">A5</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,2</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>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E6:97_1_1"/><span class="lab"><font color="Green" title="E66">A6</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default">3,2</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>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:97_1_1"><span class="lab"><font color="Green" title="E62">A2</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E7:97_1_1"/><span class="lab"><font color="Green" title="E67">A7</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97_1_1"><span class="lab"><font color="Green" title="E63">A3</font></span></a>, <a class="txt" href="#E4:97_1_1"><span class="lab"><font color="Green" title="E64">A4</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<a NAME="E8:97_1_1"/><span class="lab"><font color="Green" title="E68">A8</font></span>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 4
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:97_1_1"><span class="lab"><font color="Green" title="E63">A3</font></span></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></span>;<br/>
<span class="kw">thus </span><a NAME="E9:97_1_1"/>
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:97_1_1"><span class="lab"><font color="Green" title="E67">A7</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="aofa_000.html#D10" target="_self" title="AOFA_000:def.10">AOFA_000:def 10</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>   <a href="margrel1.html#V3" title="MARGREL1:attr.3">quasi_total</a>   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="comput_1.html#V8" title="COMPUT_1:attr.8">-ary</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<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> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, 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#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> &amp;  <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>) is  <a href="aofa_000.html#V4" title="AOFA_000:attr.4">with_catenation</a>  &amp;  <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>) is  <a href="aofa_000.html#V5" title="AOFA_000:attr.5">with_if-instruction</a>  &amp;  <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>) is  <a href="aofa_000.html#V6" title="AOFA_000:attr.6">with_while-instruction</a>  )</span><br/>

<a NAME="E10:97_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A9</font></span>: 
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (1,<a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a>,<font color="Maroon" title="c1">X</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="freealg.html#D11" title="FREEALG:def.11">FREEALG:def 11</a></span>;<br/>
<a NAME="E11:97_1_1"/><span class="lab"><font color="Green" title="E70">A10</font></span>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:97_1_1"><span class="lab"><font color="Green" title="E68">A8</font></span></a></span>;<br/>
<a NAME="E12:97_1_1"/><span class="lab"><font color="Green" title="E71">A11</font></span>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:97_1_1"><span class="lab"><font color="Green" title="E68">A8</font></span></a></span>;<br/>
<a NAME="E13:97_1_1"/><span class="lab"><font color="Green" title="E72">A12</font></span>: 
3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:97_1_1"><span class="lab"><font color="Green" title="E68">A8</font></span></a></span>;<br/>
<a NAME="E14:97_1_1"/><span class="lab"><font color="Green" title="E73">A13</font></span>: 
4 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:97_1_1"><span class="lab"><font color="Green" title="E68">A8</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c4">D</font> =  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <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> as   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>  ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">char</font> =  <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a>  as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="ordinal1.html#K4" title="ORDINAL1:func.4">omega</a>  ;<br/>
<span class="kw">set </span><font color="Maroon" title="c6">o</font> =  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (1,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>);<br/>
<a NAME="E17:97_1_1"/><span class="lab"><font color="Green" title="E74">A14</font></span>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,2</span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:97_1_1"><span class="lab"><font color="Green" title="E65">A5</font></span></a></span>;<br/>
<a NAME="E18:97_1_1"/><span class="lab"><font color="Green" title="E75">A15</font></span>: 
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,2</span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E19:97_1_1"/><span class="lab"><font color="Green" title="E76">A16</font></span>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,2</span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:97_1_1"><span class="lab"><font color="Green" title="E65">A5</font></span></a></span>;<br/>
<a NAME="E20:97_1_1"/><span class="lab"><font color="Green" title="E77">A17</font></span>: 
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a>,2</span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E21:97_1_1"/>
<font color="Maroon" title="c5">char</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:97_1_1"><span class="lab"><font color="Green" title="E74">A14</font></span></a>, <a class="txt" href="#E18:97_1_1"><span class="lab"><font color="Green" title="E75">A15</font></span></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></span>;<br/>
<a NAME="E22:97_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">char</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:97_1_1"><span class="lab"><font color="Green" title="E70">A10</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/>
<a NAME="E23:97_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A18</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (1,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</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#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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:97_1_1"><span class="lab"><font color="Green" title="E70">A10</font></span></a>, <a class="ref" href="freealg.html#D10" title="FREEALG:def.10">FREEALG:def 10</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">o</font> =  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (1,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>) as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>   <a href="margrel1.html#V3" title="MARGREL1:attr.3">quasi_total</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>,<font color="Maroon" title="c4">D</font> ;<br/>
<a NAME="E25:97_1_1"/>
 <a href="margrel1.html#K19" title="MARGREL1:func.19">arity</a> <font color="Maroon" title="c7">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:97_1_1"><span class="lab"><font color="Green" title="E78">A18</font></span></a>, <a class="ref" href="comput_1.html#T25" title="COMPUT_1:th.25">COMPUT_1:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E26:97_1_1"/>
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>   <a href="margrel1.html#V3" title="MARGREL1:attr.3">quasi_total</a>   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="comput_1.html#V8" title="COMPUT_1:attr.8">-ary</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<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> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, 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#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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:97_1_1"><span class="lab"><font color="Green" title="E69">A9</font></span></a>, <a class="ref" href="comput_1.html#D21" title="COMPUT_1:def.21">COMPUT_1:def 21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <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>) is  <a href="aofa_000.html#V4" title="AOFA_000:attr.4">with_catenation</a>  &amp;  <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>) is  <a href="aofa_000.html#V5" title="AOFA_000:attr.5">with_if-instruction</a>  &amp;  <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>) is  <a href="aofa_000.html#V6" title="AOFA_000:attr.6">with_while-instruction</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E27:97_1_1"/>
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:97_1_1"><span class="lab"><font color="Green" title="E67">A7</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="aofa_000.html#D11" target="_self" title="AOFA_000:def.11">AOFA_000:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>   <a href="margrel1.html#V3" title="MARGREL1:attr.3">quasi_total</a>  2 <a href="comput_1.html#V8" title="COMPUT_1:attr.8">-ary</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<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> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, 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#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> &amp;  <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>) is  <a href="aofa_000.html#V5" title="AOFA_000:attr.5">with_if-instruction</a>  &amp;  <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>) is  <a href="aofa_000.html#V6" title="AOFA_000:attr.6">with_while-instruction</a>  )</span><br/>

<a NAME="E28:97_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A19</font></span>: 
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (2,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="freealg.html#D11" title="FREEALG:def.11">FREEALG:def 11</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">o</font> =  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (2,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>);<br/>
<a NAME="E29:97_1_1"/>
<font color="Maroon" title="c5">char</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:97_1_1"><span class="lab"><font color="Green" title="E76">A16</font></span></a>, <a class="txt" href="#E20:97_1_1"><span class="lab"><font color="Green" title="E77">A17</font></span></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></span>;<br/>
<a NAME="E30:97_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">char</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:97_1_1"><span class="lab"><font color="Green" title="E71">A11</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/>
<a NAME="E31:97_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E80">A20</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (2,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</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#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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:97_1_1"><span class="lab"><font color="Green" title="E71">A11</font></span></a>, <a class="ref" href="freealg.html#D10" title="FREEALG:def.10">FREEALG:def 10</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c9">o</font> =  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (2,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>) as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>   <a href="margrel1.html#V3" title="MARGREL1:attr.3">quasi_total</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>,<font color="Maroon" title="c4">D</font> ;<br/>
<a NAME="E33:97_1_1"/>
 <a href="margrel1.html#K19" title="MARGREL1:func.19">arity</a> <font color="Maroon" title="c9">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E31:97_1_1"><span class="lab"><font color="Green" title="E80">A20</font></span></a>, <a class="ref" href="comput_1.html#T25" title="COMPUT_1:th.25">COMPUT_1:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E34:97_1_1"/>
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>   <a href="margrel1.html#V3" title="MARGREL1:attr.3">quasi_total</a>  2 <a href="comput_1.html#V8" title="COMPUT_1:attr.8">-ary</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<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> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, 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#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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E28:97_1_1"><span class="lab"><font color="Green" title="E79">A19</font></span></a>, <a class="ref" href="comput_1.html#D21" title="COMPUT_1:def.21">COMPUT_1:def 21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <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>) is  <a href="aofa_000.html#V5" title="AOFA_000:attr.5">with_if-instruction</a>  &amp;  <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>) is  <a href="aofa_000.html#V6" title="AOFA_000:attr.6">with_while-instruction</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E35:97_1_1"/>
3 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:97_1_1"><span class="lab"><font color="Green" title="E67">A7</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="aofa_000.html#D12" target="_self" title="AOFA_000:def.12">AOFA_000:def 12</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>   <a href="margrel1.html#V3" title="MARGREL1:attr.3">quasi_total</a>  3 <a href="comput_1.html#V8" title="COMPUT_1:attr.8">-ary</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<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> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, 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#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> &amp;  <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>) is  <a href="aofa_000.html#V6" title="AOFA_000:attr.6">with_while-instruction</a>  )</span><br/>

<a NAME="E36:97_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A21</font></span>: 
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (3,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="freealg.html#D11" title="FREEALG:def.11">FREEALG:def 11</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">o</font> =  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (3,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>);<br/>
<a NAME="E37:97_1_1"/><span class="lab"><font color="Green" title="E82">A22</font></span>: 
1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default">3,2</span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:97_1_1"><span class="lab"><font color="Green" title="E66">A6</font></span></a></span>;<br/>
<a NAME="E38:97_1_1"/><span class="lab"><font color="Green" title="E83">A23</font></span>: 
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default">3,2</span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E39:97_1_1"/><span class="lab"><font color="Green" title="E84">A24</font></span>: 
2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default">3,2</span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:97_1_1"><span class="lab"><font color="Green" title="E66">A6</font></span></a></span>;<br/>
<a NAME="E40:97_1_1"/><span class="lab"><font color="Green" title="E85">A25</font></span>: 
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default">3,2</span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T44" title="FINSEQ_1:th.44">FINSEQ_1:44</a></span>;<br/>
<a NAME="E41:97_1_1"/>
<font color="Maroon" title="c5">char</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="txt" href="#E37:97_1_1"><span class="lab"><font color="Green" title="E82">A22</font></span></a>, <a class="txt" href="#E38:97_1_1"><span class="lab"><font color="Green" title="E83">A23</font></span></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></span>;<br/>
<a NAME="E42:97_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">char</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:97_1_1"><span class="lab"><font color="Green" title="E72">A12</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/>
<a NAME="E43:97_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E86">A26</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (3,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</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#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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:97_1_1"><span class="lab"><font color="Green" title="E72">A12</font></span></a>, <a class="ref" href="freealg.html#D10" title="FREEALG:def.10">FREEALG:def 10</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">o</font> =  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (3,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>) as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>   <a href="margrel1.html#V3" title="MARGREL1:attr.3">quasi_total</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>,<font color="Maroon" title="c4">D</font> ;<br/>
<a NAME="E45:97_1_1"/>
 <a href="margrel1.html#K19" title="MARGREL1:func.19">arity</a> <font color="Maroon" title="c11">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 3
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:97_1_1"><span class="lab"><font color="Green" title="E86">A26</font></span></a>, <a class="ref" href="comput_1.html#T25" title="COMPUT_1:th.25">COMPUT_1:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E46:97_1_1"/>
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 3 is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>   <a href="margrel1.html#V3" title="MARGREL1:attr.3">quasi_total</a>  3 <a href="comput_1.html#V8" title="COMPUT_1:attr.8">-ary</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<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> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, 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#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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E36:97_1_1"><span class="lab"><font color="Green" title="E81">A21</font></span></a>, <a class="ref" href="comput_1.html#D21" title="COMPUT_1:def.21">COMPUT_1:def 21</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <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>) is  <a href="aofa_000.html#V6" title="AOFA_000:attr.6">with_while-instruction</a> </span><br/>

<span class="kw">thus </span><a NAME="E47:97_1_1"/>
4 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a>  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:97_1_1"><span class="lab"><font color="Green" title="E67">A7</font></span></a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="aofa_000.html#D13" target="_self" title="AOFA_000:def.13">AOFA_000:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 4 is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>   <a href="margrel1.html#V3" title="MARGREL1:attr.3">quasi_total</a>  2 <a href="comput_1.html#V8" title="COMPUT_1:attr.8">-ary</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<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> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, 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#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></span><br/>

<a NAME="E48:97_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E87">A27</font></span>: 
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (4,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="freealg.html#D11" title="FREEALG:def.11">FREEALG:def 11</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c12">o</font> =  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (4,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>);<br/>
<a NAME="E49:97_1_1"/>
<font color="Maroon" title="c5">char</font> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1">(<span class="default">2 <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 2</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:97_1_1"><span class="lab"><font color="Green" title="E61">A1</font></span></a>, <a class="txt" href="#E39:97_1_1"><span class="lab"><font color="Green" title="E84">A24</font></span></a>, <a class="txt" href="#E40:97_1_1"><span class="lab"><font color="Green" title="E85">A25</font></span></a>, <a class="ref" href="finseq_1.html#D7" title="FINSEQ_1:def.7">FINSEQ_1:def 7</a></span>;<br/>
<a NAME="E50:97_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">char</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 4 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:97_1_1"><span class="lab"><font color="Green" title="E73">A13</font></span></a>, <a class="ref" href="partfun1.html#D6" title="PARTFUN1:def.6">PARTFUN1:def 6</a></span>;<br/>
<a NAME="E51:97_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A28</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (4,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</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#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>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E14:97_1_1"><span class="lab"><font color="Green" title="E73">A13</font></span></a>, <a class="ref" href="freealg.html#D10" title="FREEALG:def.10">FREEALG:def 10</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">o</font> =  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> (4,<font color="Maroon" title="c5">char</font>,<font color="Maroon" title="c1">X</font>) as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>   <a href="margrel1.html#V3" title="MARGREL1:attr.3">quasi_total</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c4">D</font> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>,<font color="Maroon" title="c4">D</font> ;<br/>
<a NAME="E53:97_1_1"/>
 <a href="margrel1.html#K19" title="MARGREL1:func.19">arity</a> <font color="Maroon" title="c13">o</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E51:97_1_1"><span class="lab"><font color="Green" title="E88">A28</font></span></a>, <a class="ref" href="comput_1.html#T25" title="COMPUT_1:th.25">COMPUT_1:25</a></span>;<br/>
<span class="kw">hence </span><a NAME="E54:97_1_1"/>
 the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</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> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 4 is   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="margrel1.html#V2" title="MARGREL1:attr.2">homogeneous</a>   <a href="margrel1.html#V3" title="MARGREL1:attr.3">quasi_total</a>  2 <a href="comput_1.html#V8" title="COMPUT_1:attr.8">-ary</a>  <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <span class="p1">(<span class="default"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p2">(<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> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a></span>)</span>, 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#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>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E48:97_1_1"><span class="lab"><font color="Green" title="E87">A27</font></span></a>, <a class="ref" href="comput_1.html#D21" title="COMPUT_1:def.21">COMPUT_1:def 21</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/>


</div>
