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

<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="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">  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <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="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c2">e</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> 1 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#V8" title="COMPUT_1:attr.8">nullary</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">by</span> <span class="lab"><a class="ref" href="aofa_000.html#D10" target="_self" title="AOFA_000:def.10">Def10</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c3">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">A</font>;<br/>
<a NAME="E3:73"/>
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 <font color="Maroon" title="c1">A</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="aofa_000.html#D10" target="_self" title="AOFA_000:def.10">Def10</a></span>;<br/>
<a NAME="E4:73"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A1</font></span>: 
 <a href="pua2mss1.html#K2" title="PUA2MSS1:func.2">Den</a> <span class="p1">(<span class="default"><a href="funct_7.html#K1" title="FUNCT_7:func.1">In</a> 1,<span class="p2">(<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> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">e</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_7.html#D1" title="FUNCT_7:def.1">FUNCT_7:def 1</a></span>;<br/>
<a NAME="E5:73"/>
 <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c2">e</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="ref" href="comput_1.html#D24" title="COMPUT_1:def.24">COMPUT_1:def 24</a></span>;<br/>
<a NAME="E6:73"/><span class="kw">then </span>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">e</font> <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 <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/>
<span class="kw">hence </span><a NAME="E7:73"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <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="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:73"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="ref" href="comput_1.html#T8" title="COMPUT_1:th.8">COMPUT_1:8</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/>


</div>
