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<span class="kw">let </span><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#V3" title="AOFA_000:attr.3">with_empty-instruction</a>   <a href="aofa_000.html#V4" title="AOFA_000:attr.4">with_catenation</a>   <a href="aofa_000.html#V8" title="AOFA_000:attr.8">unital</a>   <a href="unialg_1.html#L1" title="UNIALG_1:struct.1">UAStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font> holds <br/> ( <span class="p1">(<span class="default"><a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Olive" title="b1">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">I</font> &amp; <font color="Olive" title="b1">I</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <span class="p1">(<span class="default"><a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">I</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">I</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1">(<span class="default"><a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">I</font> &amp; <font color="Maroon" title="c2">I</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <span class="p1">(<span class="default"><a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">I</font> )</span><br/>



<span class="kw">consider </span><font color="Maroon" title="c3">f</font> being  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#V10" title="COMPUT_1:attr.10">binary</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 <font color="Maroon" title="c1">A</font> <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 <font color="Maroon" title="c1">A</font><span class="kw"> such that </span><br/><a NAME="E2:78"/><span class="lab"><font color="Green" title="E48">A1</font></span>: 
<font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 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
 <span class="kw">and </span><br/><a NAME="E3:78"/><span class="lab"><font color="Green" title="E49">A2</font></span>: 
<span class="p1">(<span class="default"><a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> <span class="p2">(<span class="default"><a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,<span class="p3">(<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></span>)</span>,<font color="Maroon" title="c1">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="aofa_000.html#R1" title="AOFA_000:pred.1">is_a_unity_wrt</a> <font color="Maroon" title="c3">f</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="aofa_000.html#D15" target="_self" title="AOFA_000:def.15">Def15</a></span>;<br/>
<a NAME="E4:78"/><span class="lab"><font color="Green" title="E50">A3</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> the <a href="unialg_1.html#U1" title="UNIALG_1:sel.1">charact</a> of <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aofa_000.html#D11" target="_self" title="AOFA_000:def.11">Def11</a></span>;<br/>
<a NAME="E5:78"/>
 <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#D26" title="COMPUT_1:def.26">COMPUT_1:def 26</a></span>;<br/>
<a NAME="E6:78"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A4</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">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>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#T25" title="COMPUT_1:th.25">COMPUT_1:25</a></span>;<br/>
<a NAME="E7:78"/><span class="lab"><font color="Green" title="E52">A5</font></span>: 
 <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
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:78"><span class="lab"><font color="Green" title="E50">A3</font></span></a>, <a class="ref" href="funct_7.html#D1" title="FUNCT_7:def.1">FUNCT_7:def 1</a></span>;<br/>
<a NAME="E8:78"/>
<span class="p1"><a href="finseq_4.html#K2" title="FINSEQ_4:func.2">&lt;*</a><span class="default"><font color="Maroon" title="c2">I</font>,<font color="Maroon" title="c2">I</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#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:78"><span class="lab"><font color="Green" title="E51">A4</font></span></a>, <a class="ref" href="finseq_2.html#T157" title="FINSEQ_2:th.157">FINSEQ_2:157</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:78"/>
( <span class="p1">(<span class="default"><a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <font color="Maroon" title="c2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">I</font> &amp; <font color="Maroon" title="c2">I</font> <a href="aofa_000.html#K13" title="AOFA_000:func.13">\;</a> <span class="p1">(<span class="default"><a href="aofa_000.html#K12" title="AOFA_000:func.12">EmptyIns</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">I</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:78"><span class="lab"><font color="Green" title="E48">A1</font></span></a>, <a class="txt" href="#E3:78"><span class="lab"><font color="Green" title="E49">A2</font></span></a>, <a class="txt" href="#E7:78"><span class="lab"><font color="Green" title="E52">A5</font></span></a>, <a class="ref" href="aofa_000.html#D1" target="_self" title="AOFA_000:def.1">Def1</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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