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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>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="subset_1.html#M1">Element</a> of  <a href="coh_sp.html#K5" target="_self">MapsC</a> <font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:40"/><i><font color="Green">E21</font></i>: 
 <a href="coh_sp.html#K6" target="_self">dom</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K7" target="_self">cod</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:40"/><i><font color="Green">E22</font></i>: 
 <a href="coh_sp.html#K6" target="_self">dom</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K7" target="_self">cod</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:40"/>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span> &amp;  <a href="coh_sp.html#K6" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K6" target="_self">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="coh_sp.html#K7" target="_self">cod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K7" target="_self">cod</a> <font color="Maroon">c<sub>2</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span> &amp;  <a href="coh_sp.html#K6" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K6" target="_self">dom</a> <font color="Maroon">c<sub>2</sub></font> &amp;  <a href="coh_sp.html#K7" target="_self">cod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K7" target="_self">cod</a> <font color="Maroon">c<sub>4</sub></font> )
 
<b>by </b><i><a class="txt" href="coh_sp.html#E1:40"><i><font color="Green">E21</font></i></a>, <a class="txt" href="coh_sp.html#E2:40"><i><font color="Green">E22</font></i></a>, <a class="ref" href="coh_sp.html#T22" target="_self">Th22</a></i>;<br/>
<a NAME="E4:40"/><b>then </b>
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K2">`2</a> </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="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span> &amp;  <a href="coh_sp.html#K6" target="_self">dom</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K6" target="_self">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="coh_sp.html#K7" target="_self">cod</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K7" target="_self">cod</a> <font color="Maroon">c<sub>4</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K2">`2</a> </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="mcart_1.html#K2">`2</a> </span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span> &amp;  <a href="coh_sp.html#K6" target="_self">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K6" target="_self">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="coh_sp.html#K7" target="_self">cod</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="coh_sp.html#K7" target="_self">cod</a> <font color="Maroon">c<sub>4</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K2">`2</a> </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="mcart_1.html#K2">`2</a> </span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="mcart_1.html#K2">`2</a> </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="mcart_1.html#K2">`2</a> </span>)</span></span>)</span> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="mcart_1.html#K2">`2</a> </span>)</span> )
 
<b>by </b><i><a class="txt" href="coh_sp.html#E1:40"><i><font color="Green">E21</font></i></a>, <a class="txt" href="coh_sp.html#E2:40"><i><font color="Green">E22</font></i></a>, <a class="ref" href="coh_sp.html#T22" target="_self">Th22</a>, <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>;<br/>
<b>hence </b><a NAME="E5:40"/>
<font color="Maroon">c<sub>4</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="coh_sp.html#K9" target="_self">*</a> <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="coh_sp.html#E32"><i><font color="Green">Lemma15</font></i></a></i>;<br/>


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