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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  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>4</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</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>let </b><font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><b>that </b><br/><a NAME="E1:89"/><i><font color="Green">E58</font></i>: 
(  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font> implies (  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp;  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> ) )
 <b>and </b><br/><a NAME="E2:89"/><i><font color="Green">E59</font></i>: 
(  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>2</sub></font> implies (  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>6</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D31">WAYBEL_0:def 31</a><br/>

<a NAME="E3:89"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">c<sub>6</sub></font> <a href="relset_1.html#K10">.:</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T159">RELAT_1:159</a></i>;<br/>
<b>assume </b><a NAME="E4:89"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D31">WAYBEL_0:def 31</a><br/>

<b>hence </b><a NAME="E5:89"/>
(  <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>3</sub></font> &amp;  <a href="yellow_0.html#K1">"\/"</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="txt" href="waybel34.html#E1:89"><i><font color="Green">E58</font></i></a>, <a class="txt" href="waybel34.html#E2:89"><i><font color="Green">E59</font></i></a>, <a class="txt" href="waybel34.html#E3:89"><i><font color="Green">E60</font></i></a>, <a class="ref" href="funct_2.html#T21">FUNCT_2:21</a></i>;<br/>


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