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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be  <a href="funcop_1.html#V1">Function-yielding</a> <a href="funct_1.html#NM1">Function</a>;<br/>

<b>set </b><font color="Maroon">c<sub>4</sub></font> = <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><i><font color="Green">E13</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">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font></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">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>2</sub></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> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#D24">PBOOLE:def 24</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">c<sub>3</sub></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">c<sub>2</sub></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> <font color="Maroon">c<sub>1</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
;<br/><a NAME="E2:17_1"/><b>then </b><i><font color="Green">E14</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">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_1.html#T16">XBOOLE_1:16</a></i>;<br/><b>hence </b><i><font color="Green">E15</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">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
<br/>.= 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
;<br/><br/><b>let </b><font color="Maroon">c<sub>6</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E4:17_1"/><i><font color="Green">E16</font></i>: 
<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><a NAME="E5:17_1"/><b>then </b>
<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></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">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="autalg_1.html#E1:17_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E6:17_1"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>6</sub></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">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>;<br/><a NAME="E7:17_1"/>
<font color="Maroon">c<sub>6</sub></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">c<sub>2</sub></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">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="autalg_1.html#E2:17_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="autalg_1.html#E4:17_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E8:17_1"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>6</sub></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">c<sub>2</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="autalg_1.html#E4:17_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="autalg_1.html#E6:17_1"><i><font color="Green">E17</font></i></a>, <a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="autalg_1.html#E8:17_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="autalg_1.html#E3:17_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="autalg_1.html#E4:17_1"><i><font color="Green">E16</font></i></a>, <a class="ref" href="pboole.html#D24">PBOOLE:def 24</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:17"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="pboole.html#K12">**</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="pboole.html#K12">**</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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