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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font> be    <a href="subset_1.html#M1">Element</a> of <font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="binop_1.html#NM2">BinOp</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>







<b>assume </b><a NAME="E1:20"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<b>set </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>1</sub></font> <a href="monoid_1.html#K5" target="_self">--&gt;</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="monoid_1.html#K8" target="_self">.:</a> <font color="Maroon">c<sub>1</sub></font>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="20_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="fraenkel.html#M2">Element</a> of  <a href="fraenkel.html#K1">Funcs</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><a NAME="E1:20_1"/><i><font color="Green">E11</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="monoid_1.html#K8" target="_self">.:</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="monoid_1.html#K5" target="_self">--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>4</sub></font> <a href="monoid_1.html#K3" target="_self">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="monoid_1.html#K5" target="_self">--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="ref" href="monoid_1.html#D2" target="_self">Def2</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="monoid_1.html#K6" target="_self">[;]</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="monoid_1.html#E1:20_1"><i><font color="Green">E11</font></i></a>, <a class="ref" href="funcop_1.html#T41">FUNCOP_1:41</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="monoid_1.html#E1:20"><i><font color="Green">E10</font></i></a>, <a class="ref" href="monoid_1.html#T6" target="_self">Th6</a></i>
;<br/><b>thus </b><span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="monoid_1.html#K8" target="_self">.:</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="binop_1.html#K2">.</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="monoid_1.html#K5" target="_self">--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> = 
<font color="Maroon">c<sub>4</sub></font> <a href="monoid_1.html#K3" target="_self">.:</a> <font color="Maroon">c<sub>7</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="monoid_1.html#K5" target="_self">--&gt;</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="monoid_1.html#D2" target="_self">Def2</a></i>
<br/>.= 
<font color="Maroon">c<sub>4</sub></font> <a href="monoid_1.html#K7" target="_self">[:]</a> <font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="monoid_1.html#E1:20_1"><i><font color="Green">E11</font></i></a>, <a class="ref" href="funcop_1.html#T34">FUNCOP_1:34</a></i>
<br/>.= 
<font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="monoid_1.html#E1:20"><i><font color="Green">E10</font></i></a>, <a class="ref" href="monoid_1.html#T6" target="_self">Th6</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:20"/>
<font color="Maroon">c<sub>1</sub></font> <a href="monoid_1.html#K5" target="_self">--&gt;</a> <font color="Maroon">c<sub>3</sub></font> <a href="binop_1.html#R3">is_a_unity_wrt</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="monoid_1.html#K8" target="_self">.:</a> <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="binop_1.html#T11">BINOP_1:11</a></i>;<br/>


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