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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> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">I1</font>, <font color="Olive" title="b2">I2</font> being  <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> holds  <font color="Olive" title="b1">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Olive" title="b2">I2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 <a href="trees_4.html#K6" title="TREES_4:func.6">-tree</a> <font color="Olive" title="b1">I1</font>,<font color="Olive" title="b2">I2</font></span><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>reconsider </b><font color="Maroon" title="c3">s</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#K5" title="ORDINAL1:func.5">omega</a>  ;<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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <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#R1" title="HIDDEN:pred.1">=</a> 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></span><br/>

<a NAME="E2:101"/><i><font color="Green" title="E65">A1</font></i>: 
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>
 
<b>by </b><i><a class="ref" href="aofa_000.html#D11" target="_self" title="AOFA_000:def.11">Def11</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c7">f</font> = 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 as  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="unialg_1.html#V1" title="UNIALG_1:attr.1">homogeneous</a> <a href="unialg_1.html#V2" title="UNIALG_1:attr.2">quasi_total</a> <a href="comput_1.html#V11" title="COMPUT_1:attr.11">binary</a> <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of 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> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</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> <b>by </b><i><a class="ref" href="aofa_000.html#D11" target="_self" title="AOFA_000:def.11">Def11</a></i>;<br/>
<a NAME="E4:101"/><i><font color="Green" title="E66">A2</font></i>: 
<font color="Maroon" title="c7">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> 2,<a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a> ,<font color="Maroon" title="c1">X</font>
 
<b>by </b><i><a class="txt" href="aofa_000.html#E2:101"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="freealg.html#D12" title="FREEALG:def.12">FREEALG:def 12</a></i>;<br/>
<a NAME="E5:101"/><i><font color="Green" title="E67">A3</font></i>: 
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> 
 
<b>by </b><i><a class="ref" href="aofa_000.html#T54" target="_self" title="AOFA_000:th.54">Th54</a></i>;<br/>
<a NAME="E6:101"/><b>then </b>
<font color="Maroon" title="c3">s</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="aofa_000.html#K19" title="AOFA_000:func.19">ECIW-signature</a>  <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> 2
 
<b>by </b><i><a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>;<br/>
<a NAME="E7:101"/><b>then </b><i><font color="Green" title="E68">A4</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="freealg.html#K5" title="FREEALG:func.5">FreeOpNSG</a> 2,<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> 2 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <span class="p2">(<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></span>)</span>
 
<b>by </b><i><a class="txt" href="aofa_000.html#E5:101"><i><font color="Green" title="E67">A3</font></i></a>, <a class="ref" href="aofa_000.html#T54" target="_self" title="AOFA_000:th.54">Th54</a>, <a class="ref" href="freealg.html#D11" title="FREEALG:def.11">FREEALG:def 11</a></i>;<br/>
<a NAME="E8:101"/><i><font color="Green" title="E69">A5</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> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 2 <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <span class="p2">(<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></span>)</span>
 
<b>by </b><i><a class="ref" href="catalg_1.html#T10" title="CATALG_1:th.10">CATALG_1:10</a></i>;<br/>
<b>thus </b><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> = 
<font color="Maroon" title="c7">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</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="txt" href="aofa_000.html#E2:101"><i><font color="Green" title="E65">A1</font></i></a>, <a class="ref" href="funct_7.html#D1" title="FUNCT_7:def.1">FUNCT_7:def 1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="freealg.html#K4" title="FREEALG:func.4">Sym</a> 2,<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="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>
<b>by </b><i><a class="txt" href="aofa_000.html#E4:101"><i><font color="Green" title="E66">A2</font></i></a>, <a class="txt" href="aofa_000.html#E7:101"><i><font color="Green" title="E68">A4</font></i></a>, <a class="txt" href="aofa_000.html#E8:101"><i><font color="Green" title="E69">A5</font></i></a>, <a class="txt" href="aofa_000.html#E5:101"><i><font color="Green" title="E67">A3</font></i></a>, <a class="ref" href="freealg.html#D11" title="FREEALG:def.11">FREEALG:def 11</a></i>
<br/>.= 
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="txt" href="aofa_000.html#E5:101"><i><font color="Green" title="E67">A3</font></i></a>, <a class="ref" href="freealg.html#D10" title="FREEALG:def.10">FREEALG:def 10</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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