<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon">f</font> be  <a href="seq_1.html#V1">real-yielding</a> <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">g</font> be  <a href="seq_1.html#V1">real-yielding</a> <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">f1</font> be  <a href="seq_1.html#V1">real-yielding</a> <a href="funct_1.html#NM1">Function</a>;<br/><b>let </b><font color="Maroon">g1</font> be  <a href="seq_1.html#V1">real-yielding</a> <a href="funct_1.html#NM1">Function</a>;<br/>







<i><font color="Green">E29</font></i>:  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g</font></span>)</span> <a href="seq_1.html#K5">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g1</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="relat_1.html#K10">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K8">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="relat_1.html#K10">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g1</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">g1</font> <a href="relat_1.html#K10">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="relat_1.html#K10">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g1</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">g1</font> <a href="relat_1.html#K10">"</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">g</font> <a href="relat_1.html#K10">"</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g1</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p4">(<span class="default"><font color="Maroon">g1</font> <a href="relat_1.html#K10">"</a> <span class="p5"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="relat_1.html#K10">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g1</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">g1</font> <a href="relat_1.html#K10">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="relat_1.html#K10">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">g1</font></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p3">(<span class="default"><font color="Maroon">g1</font> <a href="relat_1.html#K10">"</a> <span class="p4"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="subset_1.html#K6">\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">g1</font></span>)</span> <a href="relat_1.html#K10">"</a> <span class="p3"><a href="tarski.html#K1">{</a><span class="default">0</span><a href="tarski.html#K1">}</a></span></span>)</span></span>)</span>
<b>by </b><i/>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">f1</font></span>)</span> <a href="rfunct_1.html#K1" target="_self">/</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
<b>by </b><i/>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="42_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:42_2"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g</font></span>)</span> <a href="seq_1.html#K5">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
 ;<br/><a NAME="E2:42_2"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>;<br/><a NAME="E3:42_2"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g1</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rfunct_1.html#D4" target="_self">Def4</a></i>;<br/><a NAME="E4:42_2"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K5">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">g1</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="rfunct_1.html#D4" target="_self">Def4</a></i>;<br/><a NAME="E5:42_2"/><b>then </b><i><font color="Green">E31</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K5">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">g1</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E6:42_2"/><b>then </b>
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">g1</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>;<br/><a NAME="E7:42_2"/><b>then </b>
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">g1</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E8:42_2"/><b>then </b>
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f</font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">f1</font></span>)</span> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">g1</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E9:42_2"/><b>then </b><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">f1</font></span>)</span> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> <a href="seq_1.html#K5">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">g1</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> )
 <b>by </b><i><a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>;<br/><a NAME="E10:42_2"/><b>then </b>
( <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">f1</font></span>)</span> &amp; <font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">g1</font></span>)</span> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> )
 <b>by </b><i/>;<br/><a NAME="E11:42_2"/><b>then </b>
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">f1</font></span>)</span></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">g1</font></span>)</span> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E12:42_2"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c</font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">f1</font></span>)</span> <a href="seq_1.html#K5">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">g1</font></span>)</span> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g</font></span>)</span> <a href="seq_1.html#K5">(#)</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g1</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_1.html#E5:42_2"><i><font color="Green">E31</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g1</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#D4" target="_self">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K5">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">g1</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="ref" href="rfunct_1.html#D4" target="_self">Def4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K5">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">g1</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_1.html#E9:42_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g1</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_1.html#E9:42_2"><i><font color="Green">E32</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">g1</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> <a href="seq_1.html#K5">(#)</a> <span class="p4">(<span class="default"><font color="Maroon">g1</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_1.html#E12:42_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> <a href="seq_1.html#K5">(#)</a> <span class="p3">(<span class="default"><font color="Maroon">g1</font> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p2">(<span class="default"><font color="Maroon">f1</font> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">g1</font></span>)</span> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">f1</font></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">g1</font></span>)</span> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_1.html#E12:42_2"><i><font color="Green">E33</font></i></a>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">f1</font></span>)</span> <a href="seq_1.html#K5">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">g</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">g1</font></span>)</span> <a href="rfunct_1.html#K3" target="_self">^</a> </span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font>
<b>by </b><i>, <a class="ref" href="seq_1.html#D5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">f1</font></span>)</span> <a href="rfunct_1.html#K1" target="_self">/</a> <span class="p2">(<span class="default"><font color="Maroon">g</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">g1</font></span>)</span></span>)</span> <a href="seq_1.html#K1">.</a> <font color="Maroon">c</font>
<b>by </b><i><a class="ref" href="rfunct_1.html#D4" target="_self">Def4</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:42"/>
<span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g</font></span>)</span> <a href="seq_1.html#K5">(#)</a> <span class="p1">(<span class="default"><font color="Maroon">f1</font> <a href="rfunct_1.html#K1" target="_self">/</a> <font color="Maroon">g1</font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">f</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">f1</font></span>)</span> <a href="rfunct_1.html#K1" target="_self">/</a> <span class="p1">(<span class="default"><font color="Maroon">g</font> <a href="seq_1.html#K5">(#)</a> <font color="Maroon">g1</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


</div>
