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<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">f</font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">q</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/><b>let </b><font color="Maroon">p</font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">D</font>;<br/>







<b>assume </b><a NAME="E1:1"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">q</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K2">rng</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span></span>)</span>
 ;<br/>

<a NAME="E2:1"/><b>then </b>
<font color="Maroon">q</font> <a href="finseq_4.html#K5">..</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T43">FINSEQ_5:43</a></i>;<br/>
<a NAME="E3:1"/><b>then </b><i><font color="Green">E32</font></i>: 
<font color="Maroon">q</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font> <a href="xxreal_0.html#R1">&lt;=</a>  <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span></span>)</span>
 
<b>by </b><i>, <a class="ref" href="finseq_4.html#T31">FINSEQ_4:31</a></i>;<br/>
<a NAME="E4:1"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="finseq_1.html#K17">|</a> <span class="p2">(<span class="default"><font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font></span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font>
 
<b>by </b><i><a class="ref" href="finseq_5.html#T19">FINSEQ_5:19</a></i>;<br/>
<b>hence </b><a NAME="E5:1"/>
<font color="Maroon">q</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">p</font> <a href="finseq_4.html#K5">..</a> <font color="Maroon">f</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>


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