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

<b>let </b><font color="Maroon" title="c1">f1</font>, <font color="Maroon" title="c2">f2</font>, <font color="Maroon" title="c3">f3</font> be  <a href="seq_1.html#V1" title="SEQ_1:attr.1">real-yielding</a> <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>





<i><font color="Green" title="E13">A1</font></i>:  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K3" title="SEQ_1:func.3">+</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K3" title="SEQ_1:func.3">+</a> <font color="Maroon" title="c2">f2</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f3</font></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D5" title="SEQ_1:def.5">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" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f3</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D3" title="SEQ_1:def.3">SEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f3</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p3">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f3</font></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c1">f1</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p2">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D5" title="SEQ_1:def.5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D5" title="SEQ_1:def.5">SEQ_1:def 5</a></i>
<br/>.= 
 <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span> <a href="seq_1.html#K3" title="SEQ_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="seq_1.html#D3" title="SEQ_1:def.3">SEQ_1:def 3</a></i>
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="16_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c4">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>assume </b><a NAME="E1:16_2"/><i><font color="Green" title="E14">A2</font></i>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K3" title="SEQ_1:func.3">+</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span>
 ;<br/><a NAME="E2:16_2"/><b>then </b>
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="rfunct_1.html#E1:16"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="seq_1.html#D3" title="SEQ_1:def.3">SEQ_1:def 3</a></i>;<br/><a NAME="E3:16_2"/><b>then </b><i><font color="Green" title="E15">A3</font></i>: 
( <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span> &amp; <font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E4:16_2"/>
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K3" title="SEQ_1:func.3">+</a> <font color="Maroon" title="c2">f2</font></span>)</span></span>)</span> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c3">f3</font></span>)</span>
 <b>by </b><i><a class="txt" href="rfunct_1.html#E1:16_2"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="seq_1.html#D5" title="SEQ_1:def.5">SEQ_1:def 5</a></i>;<br/><a NAME="E5:16_2"/><b>then </b><i><font color="Green" title="E16">A4</font></i>: 
<font color="Maroon" title="c4">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K3" title="SEQ_1:func.3">+</a> <font color="Maroon" title="c2">f2</font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K3" title="SEQ_1:func.3">+</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K3" title="SEQ_1:func.3">+</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_1.html#E1:16_2"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="seq_1.html#D5" title="SEQ_1:def.5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_1.html#E5:16_2"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="seq_1.html#D3" title="SEQ_1:def.3">SEQ_1:def 3</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span>

<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="real_1.html#K8" title="REAL_1:func.8">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">f3</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_1.html#E3:16_2"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="seq_1.html#D5" title="SEQ_1:def.5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span> <a href="real_1.html#K7" title="REAL_1:func.7">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font></span>)</span>
<b>by </b><i><a class="txt" href="rfunct_1.html#E3:16_2"><i><font color="Green" title="E15">A3</font></i></a>, <a class="ref" href="seq_1.html#D5" title="SEQ_1:def.5">SEQ_1:def 5</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span> <a href="seq_1.html#K3" title="SEQ_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span></span>)</span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <font color="Maroon" title="c4">c</font>
<b>by </b><i><a class="txt" href="rfunct_1.html#E1:16"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="rfunct_1.html#E1:16_2"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="seq_1.html#D3" title="SEQ_1:def.3">SEQ_1:def 3</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:16"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K3" title="SEQ_1:func.3">+</a> <font color="Maroon" title="c2">f2</font></span>)</span> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">f1</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span> <a href="seq_1.html#K3" title="SEQ_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">f2</font> <a href="seq_1.html#K5" title="SEQ_1:func.5">(#)</a> <font color="Maroon" title="c3">f3</font></span>)</span>
 <b>by </b><i><a class="txt" href="rfunct_1.html#E1:16"><i><font color="Green" title="E13">A1</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</a></i>;<br/>


</div>
