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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<b>given </b><font color="Maroon">c<sub>2</sub></font> being  <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_8.html#V2">algebraic</a> <a href="waybel_0.html#NM8">LATTICE</a>, <font color="Maroon">c<sub>3</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font><b> such that </b><a NAME="E1:17"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="funct_2.html#V2">onto</a>
 <b>and </b><br/><a NAME="E2:17"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="waybel_0.html#V17">infs-preserving</a>
 <b>and </b><br/><a NAME="E3:17"/><i><font color="Green">E19</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>4</sub></font> being  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> , <font color="Maroon">c<sub>5</sub></font> being  <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">c<sub>4</sub></font></span>)</span><b> such that </b><br/><a NAME="E5:17"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 <b>and </b><br/><a NAME="E6:17"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>2</sub></font>, <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>5</sub></font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 <b>by </b><i><a class="ref" href="waybel13.html#T35">WAYBEL13:35</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default"><a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>5</sub></font></span>)</span><b> such that </b><br/><a NAME="E8:17"/><i><font color="Green">E22</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is <a href="waybel_0.html#V23">isomorphic</a>
 <b>by </b><i><a class="txt" href="waybel15.html#E6:17"><i><font color="Green">E21</font></i></a>, <a class="ref" href="waybel_1.html#D8">WAYBEL_1:def 8</a></i>;<br/>
<a NAME="E9:17"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E8:17"><i><font color="Green">E22</font></i></a>, <a class="ref" href="waybel_0.html#D38">WAYBEL_0:def 38</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>7</sub></font> = <font color="Maroon">c<sub>6</sub></font> <a href="funct_1.html#K2">"</a>  as   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>,<font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="waybel15.html#E8:17"><i><font color="Green">E22</font></i></a>, <a class="ref" href="waybel_0.html#T67">WAYBEL_0:67</a></i>;<br/>
<a NAME="E11:17"/><i><font color="Green">E24</font></i>: 
<font color="Maroon">c<sub>7</sub></font> is <a href="waybel_0.html#V23">isomorphic</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E8:17"><i><font color="Green">E22</font></i></a>, <a class="ref" href="waybel_0.html#T68">WAYBEL_0:68</a></i>;<br/>
<a NAME="E12:17"/>
<font color="Maroon">c<sub>3</sub></font> <a href="waybel_1.html#NR8" target="_self">has_a_lower_adjoint</a> 
 
<b>by </b><i><a class="txt" href="waybel15.html#E2:17"><i><font color="Green">E18</font></i></a>, <a class="ref" href="waybel_1.html#T17">WAYBEL_1:17</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>8</sub></font> being   <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><b> such that </b><br/><a NAME="E14:17"/><i><font color="Green">E25</font></i>: 
<span class="p1"><a href="waybel_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>8</sub></font></span><a href="waybel_1.html#K1">]</a></span> is <a href="waybel_1.html#V3">Galois</a>
 <b>by </b><i><a class="ref" href="waybel_1.html#D11">WAYBEL_1:def 11</a></i>;<br/>
<a NAME="E15:17"/>
( <font color="Maroon">c<sub>3</sub></font> is <a href="orders_3.html#V5">monotone</a> &amp; <font color="Maroon">c<sub>8</sub></font> is <a href="orders_3.html#V5">monotone</a> )
 
<b>by </b><i><a class="txt" href="waybel15.html#E14:17"><i><font color="Green">E25</font></i></a>, <a class="ref" href="waybel_1.html#T9">WAYBEL_1:9</a></i>;<br/>
<a NAME="E16:17"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> is <a href="orders_3.html#V5">monotone</a>
 
<b>by </b><i><a class="ref" href="yellow_2.html#T14">YELLOW_2:14</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font> as  <a href="waybel_1.html#V8">kernel</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="waybel15.html#E14:17"><i><font color="Green">E25</font></i></a>, <a class="ref" href="waybel_1.html#T44">WAYBEL_1:44</a></i>;<br/>
<a NAME="E18:17"/>
<font color="Maroon">c<sub>8</sub></font> is <a href="waybel_1.html#V5">lower_adjoint</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E14:17"><i><font color="Green">E25</font></i></a>, <a class="ref" href="waybel_1.html#T10">WAYBEL_1:10</a></i>;<br/>
<a NAME="E19:17"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> is <a href="waybel_0.html#V18">sups-preserving</a>
 
<b>by </b><i><a class="ref" href="waybel_1.html#T14">WAYBEL_1:14</a></i>;<br/>
<a NAME="E20:17"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E10"><i><font color="Green">Lemma8</font></i></a></i>;<br/>
<a NAME="E21:17"/><b>then </b><i><font color="Green">E26</font></i>: 
<font color="Maroon">c<sub>9</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E3:17"><i><font color="Green">E19</font></i></a>, <a class="ref" href="waybel15.html#T13" target="_self">Th13</a></i>;<br/>
<i><font color="Green">E27</font></i>: <font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font> = 
 <a href="partfun1.html#K6">id</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="waybel15.html#E9:17"><i><font color="Green">E23</font></i></a>, <a class="ref" href="funct_1.html#T61">FUNCT_1:61</a></i>
<br/>.= 
 <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="funct_2.html#D1">FUNCT_2:def 1</a></i>
<br/>.= 
 <a href="grcat_1.html#K7">id</a> <font color="Maroon">c<sub>2</sub></font>

;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> as   <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> ;<br/>
<i><font color="Green">E28</font></i>: <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="grcat_1.html#K7">id</a> <span class="p4">(<span class="default"><a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p4">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p4">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="grcat_1.html#T12">GRCAT_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="grcat_1.html#K7">id</a> <font color="Maroon">c<sub>2</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="waybel15.html#E22:17"><i><font color="Green">E27</font></i></a>, <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="grcat_1.html#T12">GRCAT_1:12</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="quantal1.html#D9">QUANTAL1:def 9</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
;<br/>
<font color="Maroon">c<sub>10</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>10</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p4">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K1">*</a> <span class="p4">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p5">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p4">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p4">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="grcat_1.html#K7">id</a> <span class="p3">(<span class="default"><a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p4">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="waybel_1.html#T36">WAYBEL_1:36</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font>
<b>by </b><i><a class="txt" href="waybel15.html#E24:17"><i><font color="Green">E28</font></i></a>, <a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
;<br/>
<a NAME="E26:17"/><b>then </b><i><font color="Green">E29</font></i>: 
<font color="Maroon">c<sub>10</sub></font> is <a href="quantal1.html#V11">idempotent</a>
 
<b>by </b><i><a class="ref" href="quantal1.html#D9">QUANTAL1:def 9</a></i>;<br/>
<a NAME="E27:17"/><i><font color="Green">E30</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is <a href="orders_3.html#V5">monotone</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E8:17"><i><font color="Green">E22</font></i></a>, <a class="ref" href="waybel_0.html#D38">WAYBEL_0:def 38</a></i>;<br/>
<a NAME="E28:17"/><i><font color="Green">E31</font></i>: 
<font color="Maroon">c<sub>7</sub></font> is <a href="orders_3.html#V5">monotone</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E11:17"><i><font color="Green">E24</font></i></a>, <a class="ref" href="waybel_0.html#D38">WAYBEL_0:def 38</a></i>;<br/>
<a NAME="E29:17"/>
<span class="p1">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font> is <a href="orders_3.html#V5">monotone</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E27:17"><i><font color="Green">E30</font></i></a>, <a class="ref" href="yellow_2.html#T14">YELLOW_2:14</a></i>;<br/>
<a NAME="E30:17"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font> is <a href="orders_3.html#V5">monotone</a>
 
<b>by </b><i><a class="ref" href="yellow_2.html#T14">YELLOW_2:14</a></i>;<br/>
<a NAME="E31:17"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font> is <a href="orders_3.html#V5">monotone</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E28:17"><i><font color="Green">E31</font></i></a>, <a class="ref" href="yellow_2.html#T14">YELLOW_2:14</a></i>;<br/>
<a NAME="E32:17"/><b>then </b>
<font color="Maroon">c<sub>10</sub></font> is <a href="orders_3.html#V5">monotone</a>
 
<b>by </b><i><a class="ref" href="yellow_2.html#T14">YELLOW_2:14</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>10</sub></font> as  <a href="waybel_1.html#V6">projection</a> <a href="struct_0.html#NM7">Function</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <b>by </b><i><a class="txt" href="waybel15.html#E26:17"><i><font color="Green">E29</font></i></a>, <a class="ref" href="waybel_1.html#D13">WAYBEL_1:def 13</a></i>;<br/>
<b>take </b>
<font color="Maroon">c<sub>4</sub></font>
;<br/>

<b>take </b>
<font color="Maroon">c<sub>11</sub></font>
;<br/>

<a NAME="E34:17"/><i><font color="Green">E32</font></i>: 
 <a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E5:17"><i><font color="Green">E20</font></i></a>, <a class="ref" href="waybel15.html#T15" target="_self">Th15</a></i>;<br/>
<a NAME="E35:17"/>
<font color="Maroon">c<sub>6</sub></font> is <a href="waybel_0.html#V18">sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E8:17"><i><font color="Green">E22</font></i></a>, <a class="ref" href="waybel13.html#T20">WAYBEL13:20</a></i>;<br/>
<a NAME="E36:17"/><b>then </b><i><font color="Green">E33</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E10"><i><font color="Green">Lemma8</font></i></a></i>;<br/>
<a NAME="E37:17"/>
<font color="Maroon">c<sub>7</sub></font> is <a href="waybel_0.html#V18">sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E11:17"><i><font color="Green">E24</font></i></a>, <a class="ref" href="waybel13.html#T20">WAYBEL13:20</a></i>;<br/>
<a NAME="E38:17"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>7</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E10"><i><font color="Green">Lemma8</font></i></a></i>;<br/>
<a NAME="E39:17"/>
 <a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font> is <a href="waybel_0.html#V18">sups-preserving</a>
 
<b>by </b><i><a class="ref" href="waybel_1.html#T58">WAYBEL_1:58</a></i>;<br/>
<a NAME="E40:17"/><b>then </b><i><font color="Green">E35</font></i>: 
 <a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E10"><i><font color="Green">Lemma8</font></i></a></i>;<br/>
<a NAME="E41:17"/>
<span class="p1">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E34:17"><i><font color="Green">E32</font></i></a>, <a class="txt" href="waybel15.html#E36:17"><i><font color="Green">E33</font></i></a>, <a class="ref" href="waybel15.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E42:17"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E21:17"><i><font color="Green">E26</font></i></a>, <a class="ref" href="waybel15.html#T13" target="_self">Th13</a></i>;<br/>
<a NAME="E43:17"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>9</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E38:17"><i><font color="Green">E34</font></i></a>, <a class="ref" href="waybel15.html#T13" target="_self">Th13</a></i>;<br/>
<b>hence </b><a NAME="E44:17"/>
<font color="Maroon">c<sub>11</sub></font> is <a href="waybel_0.html#V22">directed-sups-preserving</a>
 <b>by </b><i><a class="txt" href="waybel15.html#E40:17"><i><font color="Green">E35</font></i></a>, <a class="ref" href="waybel15.html#T13" target="_self">Th13</a></i>;<br/>

<a NAME="E45:17"/>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>7</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="txt" href="waybel15.html#E11:17"><i><font color="Green">E24</font></i></a>, <a class="ref" href="waybel_0.html#T66">WAYBEL_0:66</a></i>;<br/>
<a NAME="E46:17"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<a NAME="E47:17"/><b>then </b><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E1:17"><i><font color="Green">E17</font></i></a>, <a class="ref" href="waybel15.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E48:17"/><b>then </b><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i><a class="ref" href="waybel15.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E49:17"/>
<span class="p1"><a href="waybel_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>7</sub></font>,<font color="Maroon">c<sub>6</sub></font></span><a href="waybel_1.html#K1">]</a></span> is <a href="waybel_1.html#V3">Galois</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E8:17"><i><font color="Green">E22</font></i></a>, <a class="ref" href="waybel15.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E50:17"/><b>then </b>
<span class="p1"><a href="waybel_1.html#K1">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<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>8</sub></font></span>)</span></span><a href="waybel_1.html#K1">]</a></span> is <a href="waybel_1.html#V3">Galois</a>
 
<b>by </b><i><a class="txt" href="waybel15.html#E14:17"><i><font color="Green">E25</font></i></a>, <a class="ref" href="waybel15.html#T7" target="_self">Th7</a></i>;<br/>
<a NAME="E51:17"/><b>then </b><i><font color="Green">E38</font></i>: 
<font color="Maroon">c<sub>1</sub></font>, <a href="yellow_2.html#K1">Image</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>8</sub></font></span>)</span> <a href="waybel_1.html#R5">are_isomorphic</a> 
 
<b>by </b><i><a class="txt" href="waybel15.html#E47:17"><i><font color="Green">E36</font></i></a>, <a class="ref" href="waybel15.html#T6" target="_self">Th6</a></i>;<br/>
<a NAME="E52:17"/><i><font color="Green">E39</font></i>: 
 <a href="relset_1.html#K4">dom</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>8</sub></font></span>)</span> <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="E53:17"/><i><font color="Green">E40</font></i>: 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_4"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>12</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:17_4"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/><a NAME="E2:17_4"/><b>then </b>
<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>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</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>5</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="funct_2.html#T7">FUNCT_2:7</a></i>;<br/><b>hence </b><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>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> = 
<span class="p1">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="funct_1.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>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="tmap_1.html#T91">TMAP_1:91</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <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>8</sub></font></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="txt" href="waybel15.html#E52:17"><i><font color="Green">E39</font></i></a>, <a class="txt" href="waybel15.html#E1:17_4"><i><font color="Green">E41</font></i></a>, <a class="ref" href="funct_1.html#T23">FUNCT_1:23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
;<br/><br/></div><b>end;</b></div>
<a NAME="E55:17"/><b>then </b>
 <a href="relset_1.html#K5">rng</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>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel15.html#E52:17"><i><font color="Green">E39</font></i></a>, <a class="txt" href="waybel15.html#E53:17"><i><font color="Green">E40</font></i></a>, <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>
<a NAME="E56:17"/><b>then </b><i><font color="Green">E41</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</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="E57:17"/>
 <a href="yellow_0.html#K5">subrelstr</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <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>8</sub></font></span>)</span></span>)</span> is  <a href="orders_2.html#V1">strict</a> <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of  <a href="yellow_1.html#K3">BoolePoset</a> <font color="Maroon">c<sub>4</sub></font>
 
<b>by </b><i><a class="ref" href="waybel15.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E58:17"/><b>then </b>
 <a href="yellow_0.html#K5">subrelstr</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <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>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K5">subrelstr</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="waybel15.html#E56:17"><i><font color="Green">E41</font></i></a>, <a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/>
<a NAME="E59:17"/><b>then </b><i><font color="Green">E42</font></i>: 
 <a href="yellow_0.html#K5">subrelstr</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <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>8</sub></font></span>)</span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_2.html#K1">Image</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
 
;<br/>
<i><font color="Green">E43</font></i>:  <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> = 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="txt" href="waybel15.html#E48:17"><i><font color="Green">E37</font></i></a>, <a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>
<br/>.= 
 <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
;<br/>
<font color="Maroon">c<sub>11</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>7</sub></font> <a href="partfun1.html#K1">*</a> <span class="p3">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>7</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <span class="p2">(<span class="default"><a href="waybel_1.html#K2">corestr</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T55">RELAT_1:55</a></i>
;<br/>
<a NAME="E62:17"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>11</sub></font>
 
<b>by </b><i><a class="txt" href="waybel15.html#E60:17"><i><font color="Green">E43</font></i></a>, <a class="ref" href="relat_1.html#T47">RELAT_1:47</a></i>;<br/>
<b>then </b> <a href="yellow_2.html#K1">Image</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel_1.html#K3">inclusion</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="partfun1.html#K1">*</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> = 
 <a href="yellow_0.html#K5">subrelstr</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>11</sub></font></span>)</span>

<br/>.= 
 <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>11</sub></font>

;<br/>
<b>hence </b><a NAME="E64:17"/>
<font color="Maroon">c<sub>1</sub></font>, <a href="yellow_2.html#K1">Image</a> <font color="Maroon">c<sub>11</sub></font> <a href="waybel_1.html#R5">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="waybel15.html#E51:17"><i><font color="Green">E38</font></i></a>, <a class="txt" href="waybel15.html#E59:17"><i><font color="Green">E42</font></i></a></i>;<br/>


</div>
