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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="funct_1.html#NM1">Function</a>;<br/>

<b>assume </b><a NAME="E1:43_2_1"/><i><font color="Green">E21</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> st  <a href="tarski.html#K3">union</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K9">.:</a> <font color="Olive">b<sub>1</sub></font></span>)</span>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="cohsp_1.html#D10" target="_self">COHSP_1:def 10</a><br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="subset_1.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="cohsp_1.html#D11" target="_self">COHSP_1:def 11</a><br/>

<b>thus </b><a NAME="E2:43_2_1"/>
( <font color="Maroon">c<sub>2</sub></font> is <a href="cohsp_1.html#V1" target="_self">c=directed</a> &amp;  <a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>1</sub></font> implies <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="tarski.html#K3">union</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="tarski.html#K3">union</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="relat_1.html#K9">.:</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="cohsp_1.html#E1:43_2_1"><i><font color="Green">E21</font></i></a></i>;<br/>


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