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<b>let </b><font color="Maroon" title="c1">A</font> be  <a href="unialg_1.html#V8" title="UNIALG_1:attr.8">non-empty</a> <a href="aofa_000.html#V4" title="AOFA_000:attr.4">with_catenation</a> <a href="aofa_000.html#V7" title="AOFA_000:attr.7">associative</a>  <a href="unialg_1.html#L1" title="UNIALG_1:struct.1">UAStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">I1</font>, <font color="Maroon" title="c3">I2</font>, <font color="Maroon" title="c4">I3</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font>;<br/>



<b>reconsider </b><font color="Maroon" title="c5">f</font> = the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">A</font> <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="aofa_000.html#V1" title="AOFA_000:attr.1">associative</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 <font color="Maroon" title="c1">A</font> <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 <font color="Maroon" title="c1">A</font> <b>by </b><i><a class="ref" href="aofa_000.html#D14" target="_self" title="AOFA_000:def.14">Def14</a></i>;<br/>
<a NAME="E2:79"/>
( 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 <font color="Maroon" title="c1">A</font> &amp;  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c5">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 
<b>by </b><i><a class="ref" href="aofa_000.html#D11" target="_self" title="AOFA_000:def.11">Def11</a>, <a class="ref" href="comput_1.html#D26" title="COMPUT_1:def.26">COMPUT_1:def 26</a></i>;<br/>
<a NAME="E3:79"/><b>then </b>
(  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">f</font> <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 <font color="Maroon" title="c1">A</font> &amp;  <a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 2,<span class="p1">(<span class="default"><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 <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2 )
 
<b>by </b><i><a class="ref" href="comput_1.html#T25" title="COMPUT_1:th.25">COMPUT_1:25</a>, <a class="ref" href="funct_7.html#D1" title="FUNCT_7:def.1">FUNCT_7:def 1</a></i>;<br/>
<a NAME="E4:79"/><b>then </b>
( <font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">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="c2">I1</font>,<font color="Maroon" title="c3">I2</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> &amp; <font color="Maroon" title="c3">I2</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c4">I3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">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="c3">I2</font>,<font color="Maroon" title="c4">I3</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</font></span>)</span> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c4">I3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">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"><span class="p2">(<span class="default"><font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</font></span>)</span>,<font color="Maroon" title="c4">I3</font></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> &amp; <font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I2</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c4">I3</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">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="c2">I1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">I2</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c4">I3</font></span>)</span></span><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">*&gt;</a></span> &amp; <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c2">I1</font>,<font color="Maroon" title="c3">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>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">f</font> &amp; <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c3">I2</font>,<font color="Maroon" title="c4">I3</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>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">f</font> &amp; <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c2">I1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">I2</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c4">I3</font></span>)</span></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>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">f</font> &amp; <span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</font></span>)</span>,<font color="Maroon" title="c4">I3</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>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">f</font> )
 
<b>by </b><i><a class="ref" href="catalg_1.html#T10" title="CATALG_1:th.10">CATALG_1:10</a></i>;<br/>
<b>hence </b><a NAME="E5:79"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c3">I2</font></span>)</span> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c4">I3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">I1</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">I2</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c4">I3</font></span>)</span>
 <b>by </b><i><a class="ref" href="aofa_000.html#D2" target="_self" title="AOFA_000:def.2">Def2</a></i>;<br/>


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