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<a NAME="E1:74_1_1"/><span class="lab"><font color="Green" title="E39">A1</font></span>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> <font color="Maroon" title="c2">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font> <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#T40" target="_self" title="COMPUT_1:th.40">Th40</a></span>;<br/>
<a NAME="E2:74_1_1"/>
<font color="Maroon" title="c1">n</font> <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> <font color="Maroon" title="c2">i</font> is  <a href="comput_1.html#V2" title="COMPUT_1:attr.2">len-total</a> 
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="74_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="comput_1.html#D3" target="_self" title="COMPUT_1:def.3">COMPUT_1:def 3</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">y</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> <font color="Maroon" title="c2">i</font></span>)</span> implies <font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> <font color="Maroon" title="c2">i</font></span>)</span> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:74_1_1_1"/><span class="lab"><font color="Green" title="E40">A2</font></span>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c4">y</font>
 <span class="kw">and </span><br/><a NAME="E2:74_1_1_1"/><span class="lab"><font color="Green" title="E41">A3</font></span>: 
<font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> <font color="Maroon" title="c2">i</font></span>)</span>
 ; <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="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> <font color="Maroon" title="c2">i</font></span>)</span></span><br/>

<a NAME="E3:74_1_1_1"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">n</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74_1_1"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="txt" href="#E2:74_1_1_1"><span class="lab"><font color="Green" title="E41">A3</font></span></a>, <a class="ref" href="finseq_1.html#D18" title="FINSEQ_1:def.18">FINSEQ_1:def 18</a></span>;<br/>
<a NAME="E4:74_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c4">y</font> is    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of <font color="Maroon" title="c1">n</font> <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="#E1:74_1_1_1"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="ref" href="finseq_2.html#T110" title="FINSEQ_2:th.110">FINSEQ_2:110</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:74_1_1_1"/>
<font color="Maroon" title="c4">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> <font color="Maroon" title="c2">i</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74_1_1"><span class="lab"><font color="Green" title="E39">A1</font></span></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><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:74_1_1"/>
( <font color="Maroon" title="c1">n</font> <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> <font color="Maroon" title="c2">i</font> is  <a href="comput_1.html#V2" title="COMPUT_1:attr.2">len-total</a>  &amp; not <font color="Maroon" title="c1">n</font> <a href="comput_1.html#K5" title="COMPUT_1:func.5">proj</a> <font color="Maroon" title="c2">i</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74_1_1"><span class="lab"><font color="Green" title="E39">A1</font></span></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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