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<span class="kw">let </span><font color="Maroon" title="c1">P</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="comput_1.html#V6" title="COMPUT_1:attr.6">primitive-recursively_closed</a>  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="comput_1.html#K2" title="COMPUT_1:func.2">HFuncs</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font></span><br/>

<span class="kw">reconsider </span><font color="Maroon" title="c2">F</font> =  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <a href="comput_1.html#V3" title="COMPUT_1:attr.3">with_the_same_arity</a>   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <span class="p1">(<span class="default"><a href="comput_1.html#K2" title="COMPUT_1:func.2">HFuncs</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a></span>)</span> <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  <span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#T49" title="FINSEQ_1:th.49">FINSEQ_1:49</a></span>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">f</font> = <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>;<br/>
<a NAME="E2:117"/><span class="lab"><font color="Green" title="E79">A1</font></span>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c1">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T2" title="XBOOLE_1:th.2">XBOOLE_1:2</a></span>;<br/>
<a NAME="E3:117"/><span class="lab"><font color="Green" title="E80">A2</font></span>: 
 <a href="margrel1.html#K19" title="MARGREL1:func.19">arity</a> <span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <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#T32" target="_self" title="COMPUT_1:th.32">Th35</a></span>;<br/>
<a NAME="E4:117"/><span class="lab"><font color="Green" title="E81">A3</font></span>: 
<font color="Maroon" title="c1">P</font> is  <a href="comput_1.html#V4" title="COMPUT_1:attr.4">composition_closed</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#D14" target="_self" title="COMPUT_1:def.14">Def17</a></span>;<br/>
<a NAME="E5:117"/>
<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#T69" target="_self" title="COMPUT_1:th.69">Th73</a></span>;<br/>
<a NAME="E6:117"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> <a href="comput_1.html#K3" title="COMPUT_1:func.3">const</a> <a href="numbers.html#K6" title="NUMBERS:func.6">0</a></span>)</span> <a href="funct_1.html#NK3" title="FUNCT_1:NK.3">*</a> <span class="p1"><a href="funct_6.html#K6" title="FUNCT_6:func.6">&lt;:</a><span class="default"><font color="Maroon" title="c2">F</font></span><a href="funct_6.html#K6" title="FUNCT_6:func.6">:&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:117"><span class="lab"><font color="Green" title="E80">A2</font></span></a>, <a class="txt" href="#E2:117"><span class="lab"><font color="Green" title="E79">A1</font></span></a>, <a class="txt" href="#E4:117"><span class="lab"><font color="Green" title="E81">A3</font></span></a>, <a class="ref" href="comput_1.html#D12" target="_self" title="COMPUT_1:def.12">Def15</a>, <a class="ref" href="card_1.html#T27" title="CARD_1:th.27">CARD_1:27</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:117"/>
 <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">P</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_6.html#T40" title="FUNCT_6:th.40">FUNCT_6:40</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/>


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