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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#V3">transitive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</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>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:20"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_0.html#V17">infs-preserving</a>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D32">WAYBEL_0:def 32</a><br/>

<a NAME="E2:20"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="waybel_0.html#R3">preserves_inf_of</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="txt" href="waybel20.html#E1:20"><i><font color="Green">E18</font></i></a>, <a class="ref" href="waybel_0.html#D32">WAYBEL_0:def 32</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>4</sub></font> =  <a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>2</sub></font>;<br/>
<a NAME="E3:20"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#R1">=</a>  <a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="waybel_1.html#T32">WAYBEL_1:32</a></i>;<br/>
<b>assume </b><a NAME="E4:20"/><i><font color="Green">E21</font></i>: 
 <a href="yellow_0.html#R2">ex_inf_of</a> <font color="Maroon">c<sub>3</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#D30">WAYBEL_0:def 30</a><br/>

<a NAME="E5:20"/><b>then </b><i><font color="Green">E22</font></i>: 
 <a href="yellow_0.html#R2">ex_inf_of</a> <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="waybel20.html#E2:20"><i><font color="Green">E19</font></i></a>, <a class="ref" href="waybel_0.html#D30">WAYBEL_0:def 30</a></i>;<br/>
<a NAME="E6:20"/><i><font color="Green">E23</font></i>: 
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel20.html#E2:20"><i><font color="Green">E19</font></i></a>, <a class="txt" href="waybel20.html#E4:20"><i><font color="Green">E21</font></i></a>, <a class="ref" href="waybel_0.html#D30">WAYBEL_0:def 30</a></i>;<br/>
<a NAME="E7:20"/><i><font color="Green">E24</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>2</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/>
<a NAME="E8:20"/><i><font color="Green">E25</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/>
<a NAME="E9:20"/><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R2">in</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="txt" href="waybel20.html#E7:20"><i><font color="Green">E24</font></i></a>, <a class="ref" href="funct_1.html#D5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> ;<br/>
<a NAME="E11:20"/>
 <a href="yellow_0.html#K2">"/\"</a> <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>1</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel20.html#E2:20"><i><font color="Green">E19</font></i></a>, <a class="txt" href="waybel20.html#E3:20"><i><font color="Green">E20</font></i></a>, <a class="txt" href="waybel20.html#E4:20"><i><font color="Green">E21</font></i></a>, <a class="txt" href="waybel20.html#E8:20"><i><font color="Green">E25</font></i></a>, <a class="txt" href="waybel20.html#E9:20"><i><font color="Green">E26</font></i></a>, <a class="ref" href="waybel_0.html#D30">WAYBEL_0:def 30</a></i>;<br/>
<b>hence </b><a NAME="E12:20"/>
 <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>3</sub></font>, <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="waybel20.html#E3:20"><i><font color="Green">E20</font></i></a>, <a class="txt" href="waybel20.html#E5:20"><i><font color="Green">E22</font></i></a>, <a class="ref" href="yellow_0.html#T64">YELLOW_0:64</a></i>;<br/>

<b>thus </b><a NAME="E13:20"/>
 <a href="yellow_0.html#NK4" target="_self">inf</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="relset_1.html#K10">.:</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK4" target="_self">inf</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel20.html#E3:20"><i><font color="Green">E20</font></i></a>, <a class="txt" href="waybel20.html#E5:20"><i><font color="Green">E22</font></i></a>, <a class="txt" href="waybel20.html#E6:20"><i><font color="Green">E23</font></i></a>, <a class="ref" href="yellow_0.html#T64">YELLOW_0:64</a></i>;<br/>


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