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<b>let </b><font color="Maroon">q</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="relat_1.html#V2">non-empty</a> <a href="finseq_1.html#NM1">FinSequence</a>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="funct_7.html#M2" target="_self">FuncSequence</a> of <font color="Maroon">q</font>;<br/>



<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:95_1"/>
( <font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a>  or <font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1_1"><b>suppose </b></a><a NAME="E1:95_1_1"/>
<font color="Maroon">p</font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:95_1_1"/><b>then </b>
(  <a href="funct_7.html#K4" target="_self">compose</a> <font color="Maroon">p</font>,<span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1</span>)</span> <a href="hidden.html#R1">=</a>  <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default"><font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1</span>)</span> &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> 0 &amp;  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 )
 <b>by </b><i>, , <a class="ref" href="finseq_1.html#T25">FINSEQ_1:25</a></i>;<br/><b>hence </b><a NAME="E3:95_1_1"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_7.html#K4" target="_self">compose</a> <font color="Maroon">p</font>,<span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1 &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_7.html#K4" target="_self">compose</a> <font color="Maroon">p</font>,<span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font></span>)</span> )
 <b>by </b><i><a class="ref" href="relat_1.html#T71">RELAT_1:71</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="95_1_2"><b>suppose </b></a><a NAME="E1:95_1_2"/>
<font color="Maroon">p</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a> 
 ;<br/><div class="add"><a NAME="E2:95_1_2"/><b>then </b>
(  <a href="funct_7.html#K6" target="_self">firstdom</a> <font color="Maroon">p</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1 &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_7.html#K4" target="_self">compose</a> <font color="Maroon">p</font>,<span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="funct_7.html#K7" target="_self">lastrng</a> <font color="Maroon">p</font> &amp;  <a href="funct_7.html#K7" target="_self">lastrng</a> <font color="Maroon">p</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font></span>)</span> )
 <b>by </b><i>, </i>;<br/><b>hence </b><a NAME="E3:95_1_2"/>
(  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="funct_7.html#K4" target="_self">compose</a> <font color="Maroon">p</font>,<span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1 &amp;  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><a href="funct_7.html#K4" target="_self">compose</a> <font color="Maroon">p</font>,<span class="p2">(<span class="default"><font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1">c=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font></span>)</span> )
 <b>by </b><i>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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