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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/>





<b>assume </b><a NAME="E1:9"/><i><font color="Green">E5</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="yellow_9.html#K1">incl</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="funct_2.html#R2">=</a>  <a href="grcat_1.html#K7">id</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E2:9"/><b>then </b><i><font color="Green">E6</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="yellow16.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E3:9"/><i><font color="Green">E7</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a></i>;<br/>
<a NAME="E4:9"/><b>then </b>
 <a href="yellow_9.html#K1">incl</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font> <a href="funct_2.html#R1">=</a>  <a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="yellow_9.html#D1">YELLOW_9:def 1</a></i>;<br/>
<a NAME="E5:9"/><b>then </b>
<span class="p1">(<span class="default"><a href="yellow_9.html#K1">incl</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_2.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>;<br/>
<b>then </b><i><font color="Green">E8</font></i>: <font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> = 
<span class="p1">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="yellow16.html#E1:9"><i><font color="Green">E5</font></i></a>, <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="partfun1.html#K6">id</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font>

<br/>.= 
<font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="ref" href="funct_2.html#T23">FUNCT_2:23</a></i>
;<br/>
<a NAME="E7:9"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <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>hence </b><a NAME="E8:9"/>
<font color="Maroon">c<sub>3</sub></font> is  <a href="quantal1.html#V11">idempotent</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="yellow16.html#E2:9"><i><font color="Green">E6</font></i></a>, <a class="txt" href="yellow16.html#E3:9"><i><font color="Green">E7</font></i></a>, <a class="txt" href="yellow16.html#E6:9"><i><font color="Green">E8</font></i></a>, <a class="ref" href="funct_2.html#T4">FUNCT_2:4</a>, <a class="ref" href="quantal1.html#D9">QUANTAL1:def 9</a></i>;<br/>


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