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<span class="kw">let </span><font color="Maroon" title="c1">f</font>, <font color="Maroon" title="c2">g</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="comput_1.html#K2" title="COMPUT_1:func.2">HFuncs</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</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">F</font> being  <a href="comput_1.html#V3" title="COMPUT_1:attr.3">with_the_same_arity</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="comput_1.html#K2" title="COMPUT_1:func.2">HFuncs</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>   st <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f</font> <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="Olive" title="b1">F</font></span><a href="funct_6.html#K6" title="FUNCT_6:func.6">:&gt;</a></span> holds <br/> <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K1" title="COMPUT_1:func.1">arity</a> <font color="Olive" title="b1">F</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">F</font> be   <a href="comput_1.html#V3" title="COMPUT_1:attr.3">with_the_same_arity</a>   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="comput_1.html#K2" title="COMPUT_1:func.2">HFuncs</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f</font> <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="c3">F</font></span><a href="funct_6.html#K6" title="FUNCT_6:func.6">:&gt;</a></span> implies  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K1" title="COMPUT_1:func.1">arity</a> <font color="Maroon" title="c3">F</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:86"/>
<font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">f</font> <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="c3">F</font></span><a href="funct_6.html#K6" title="FUNCT_6:func.6">:&gt;</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K1" title="COMPUT_1:func.1">arity</a> <font color="Maroon" title="c3">F</font></span><br/>

<a NAME="E2:86"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c2">g</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="comput_1.html#K1" title="COMPUT_1:func.1">arity</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="comput_1.html#T46" target="_self" title="COMPUT_1:th.46">Th46</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">x</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <span class="kw"> such that </span><br/><a NAME="E4:86"/><span class="lab"><font color="Green" title="E46">A2</font></span>: 
<font color="Maroon" title="c4">x</font> <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="c2">g</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_0.html#D1" title="XBOOLE_0:def.1">XBOOLE_0:def 1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c5">x</font> = <font color="Maroon" title="c4">x</font> as    <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#K1" title="COMPUT_1:func.1">arity</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="finseq_2.html#K4" title="FINSEQ_2:func.4">-tuples_on</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:86"><span class="lab"><font color="Green" title="E45">A1</font></span></a>, <a class="txt" href="#E4:86"><span class="lab"><font color="Green" title="E46">A2</font></span></a></span>;<br/>
<a NAME="E6:86"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K1" title="COMPUT_1:func.1">arity</a> <font color="Maroon" title="c3">F</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D18" title="FINSEQ_1:def.18">FINSEQ_1:def 18</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:86"/>
 <a href="unialg_1.html#K3" title="UNIALG_1:func.3">arity</a> <font color="Maroon" title="c2">g</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="comput_1.html#K1" title="COMPUT_1:func.1">arity</a> <font color="Maroon" title="c3">F</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:86"><span class="lab"><font color="Green" title="E46">A2</font></span></a>, <a class="ref" href="unialg_1.html#D10" title="UNIALG_1:def.10">UNIALG_1:def 10</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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