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<div class="add">

<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="unialg_2.html#M3" target="_self">SubAlgebra</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><a NAME="E1:25"/><i><font color="Green">E16</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/>

<b>hence </b><a NAME="E2:25"/>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>3</sub></font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_2.html#D8" target="_self">UNIALG_2:def 8</a><br/>

<b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="unialg_2.html#D8" target="_self">Def8</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="unialg_2.html#D8" target="_self">Def8</a></i>;<br/>
<a NAME="E5:25"/><i><font color="Green">E17</font></i>: 
( the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a> &amp; the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a> )
 
<b>by </b><i><a class="ref" href="unialg_2.html#D8" target="_self">Def8</a></i>;<br/>
<b>let </b><font color="Maroon">c<sub>6</sub></font> be  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<b>assume </b><a NAME="E6:25"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>6</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>
 ;<br/>

<a NAME="E7:25"/><i><font color="Green">E19</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>3</sub></font> )
 
<b>by </b><i><a class="ref" href="unialg_2.html#D7" target="_self">Def7</a>, <a class="ref" href="unialg_2.html#T10" target="_self">Th10</a></i>;<br/>
<a NAME="E8:25"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">c<sub>6</sub></font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">c<sub>3</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_2.html#D5" target="_self">UNIALG_2:def 5</a><br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>6</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="unialg_2.html#D4" target="_self">UNIALG_2:def 4</a><br/>



<b>assume </b><a NAME="E1:25_1"/><i><font color="Green">E21</font></i>: 
 <a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K3">len</a> <font color="Maroon">c<sub>8</sub></font>
 ;<br/>

<a NAME="E2:25_1"/>
( <font color="Maroon">c<sub>6</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> &amp;  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>6</sub></font> )
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<a NAME="E3:25_1"/><b>then </b><i><font color="Green">E22</font></i>: 
(  <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</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="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E4:25_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of <font color="Maroon">c<sub>5</sub></font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>9</sub></font> = <font color="Maroon">c<sub>8</sub></font> as    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">c<sub>5</sub></font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>8</sub></font> as    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">c<sub>4</sub></font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="txt" href="unialg_2.html#E6:25"><i><font color="Green">E18</font></i></a>, <a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<a NAME="E7:25_1"/>
 <a href="relat_1.html#K2">rng</a> <font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</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="txt" href="unialg_2.html#E3:25_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E8:25_1"/><b>then </b>
<font color="Maroon">c<sub>8</sub></font> is    <a href="finseq_1.html#M2">FinSequence</a> of 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="finseq_1.html#D4">FINSEQ_1:def 4</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>8</sub></font> as    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K3">*</a>  <b>by </b><i><a class="ref" href="finseq_1.html#D11">FINSEQ_1:def 11</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E11:25_1"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>3</sub></font> &amp; the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>by </b><i><a class="ref" href="finseq_2.html#T11">FINSEQ_2:11</a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>13</sub></font> = the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>12</sub></font> as   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="unialg_2.html#E7:25"><i><font color="Green">E19</font></i></a>, <a class="txt" href="unialg_2.html#E11:25_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="unialg_2.html#T6" target="_self">Th6</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>14</sub></font> = <span class="p1">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>5</sub></font>;<br/>
<b>set </b><font color="Maroon">c<sub>15</sub></font> = <span class="p1">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E13:25_1"/><i><font color="Green">E24</font></i>: 
( <span class="p1">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">c<sub>5</sub></font> <a href="finseq_2.html#K3">*</a>  :  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>13</sub></font> </span>}</span>  &amp; <span class="p1">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is    <a href="finseq_2.html#M2">Element</a> of <font color="Maroon">c<sub>4</sub></font> <a href="finseq_2.html#K3">*</a>  :  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>13</sub></font> </span>}</span>  &amp; <span class="p1">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is    <a href="finseq_2.html#M2">Element</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="finseq_2.html#K3">*</a>  :  <a href="finseq_1.html#K3">len</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>13</sub></font> </span>}</span>  )
 
<b>by </b><i><a class="ref" href="finseq_2.html#D4">FINSEQ_2:def 4</a></i>;<br/>
<a NAME="E14:25_1"/><i><font color="Green">E25</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">c<sub>13</sub></font> )
 
<b>by </b><i><a class="txt" href="unialg_2.html#E5:25"><i><font color="Green">E17</font></i></a>, <a class="ref" href="unialg_2.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E15:25_1"/><i><font color="Green">E26</font></i>: 
 <a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E11:25_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="unialg_2.html#T9" target="_self">Th9</a></i>;<br/>
<i><font color="Green">E27</font></i>: <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>13</sub></font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">c<sub>5</sub></font>
<b>by </b><i><a class="txt" href="unialg_2.html#E5:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="unialg_2.html#E11:25_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="unialg_2.html#D7" target="_self">Def7</a></i>
<br/>.= 
<font color="Maroon">c<sub>13</sub></font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>5</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="unialg_2.html#E14:25_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="unialg_2.html#D6" target="_self">Def6</a></i>
;<br/>
<a NAME="E17:25_1"/>
( <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> )
 
<b>by </b><i><a class="txt" href="unialg_2.html#E1:25_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="unialg_2.html#E13:25_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="unialg_2.html#E15:25_1"><i><font color="Green">E26</font></i></a></i>;<br/>
<a NAME="E18:25_1"/><b>then </b>
<font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>13</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>10</sub></font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E16:25_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="funct_1.html#T72">FUNCT_1:72</a></i>;<br/>
<b>hence </b><a NAME="E19:25_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E6:25"><i><font color="Green">E18</font></i></a>, <a class="txt" href="unialg_2.html#E1:25_1"><i><font color="Green">E21</font></i></a>, <a class="txt" href="unialg_2.html#E14:25_1"><i><font color="Green">E25</font></i></a>, <a class="txt" href="unialg_2.html#E15:25_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="unialg_2.html#D4" target="_self">Def4</a></i>;<br/>


</div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>assume </b><a NAME="E1:25_2"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>1</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> = the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>1</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> as   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="unialg_2.html#T6" target="_self">Th6</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>9</sub></font> = the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> as   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="unialg_2.html#E7:25"><i><font color="Green">E19</font></i></a>, <a class="txt" href="unialg_2.html#E1:25_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="unialg_2.html#T6" target="_self">Th6</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> as   <a href="unialg_2.html#NM5">operation</a> of <font color="Maroon">c<sub>3</sub></font> <b>by </b><i><a class="txt" href="unialg_2.html#E7:25"><i><font color="Green">E19</font></i></a>, <a class="txt" href="unialg_2.html#E1:25_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="unialg_2.html#T6" target="_self">Th6</a></i>;<br/><a NAME="E5:25_2"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="unialg_2.html#E5:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="unialg_2.html#E7:25"><i><font color="Green">E19</font></i></a>, <a class="txt" href="unialg_2.html#E1:25_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="unialg_2.html#D7" target="_self">Def7</a></i>;<br/><a NAME="E6:25_2"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>6</sub></font> <a href="unialg_2.html#R2" target="_self">is_closed_on</a> <font color="Maroon">c<sub>10</sub></font> )
 <b>by </b><i><a class="txt" href="unialg_2.html#E5:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="unialg_2.html#E8:25"><i><font color="Green">E20</font></i></a>, <a class="ref" href="unialg_2.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E7:25_2"/><i><font color="Green">E24</font></i>: 
 <a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a>  <a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>8</sub></font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E7:25"><i><font color="Green">E19</font></i></a>, <a class="txt" href="unialg_2.html#E1:25_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="unialg_2.html#T9" target="_self">Th9</a></i>;<br/><b>thus </b>the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font> = 
<font color="Maroon">c<sub>8</sub></font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">c<sub>4</sub></font>
<b>by </b><i><a class="txt" href="unialg_2.html#E5:25"><i><font color="Green">E17</font></i></a>, <a class="txt" href="unialg_2.html#E7:25"><i><font color="Green">E19</font></i></a>, <a class="txt" href="unialg_2.html#E1:25_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="unialg_2.html#D7" target="_self">Def7</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="unialg_2.html#E6:25_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="unialg_2.html#D6" target="_self">Def6</a></i>
<br/>.= 
<font color="Maroon">c<sub>8</sub></font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="xboole_0.html#K3">/\</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="unialg_2.html#E1:25"><i><font color="Green">E16</font></i></a>, <a class="ref" href="unialg_2.html#T1" target="_self">Th1</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="partfun1.html#K2">|</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="unialg_2.html#E6:25"><i><font color="Green">E18</font></i></a>, <a class="ref" href="relat_1.html#T100">RELAT_1:100</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="unialg_1.html#K2">arity</a> <font color="Maroon">c<sub>8</sub></font></span>)</span> <a href="finseq_2.html#K4">-tuples_on</a> <font color="Maroon">c<sub>6</sub></font></span>)</span>
<b>by </b><i><a class="txt" href="unialg_2.html#E6:25_2"><i><font color="Green">E23</font></i></a>, <a class="ref" href="unialg_2.html#D6" target="_self">Def6</a></i>
<br/>.= 
<font color="Maroon">c<sub>10</sub></font> <a href="unialg_2.html#K2" target="_self">/.</a> <font color="Maroon">c<sub>6</sub></font>
<b>by </b><i><a class="txt" href="unialg_2.html#E5:25_2"><i><font color="Green">E22</font></i></a>, <a class="txt" href="unialg_2.html#E6:25_2"><i><font color="Green">E23</font></i></a>, <a class="txt" href="unialg_2.html#E7:25_2"><i><font color="Green">E24</font></i></a>, <a class="ref" href="unialg_2.html#D6" target="_self">Def6</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>7</sub></font>
<b>by </b><i><a class="txt" href="unialg_2.html#E7:25"><i><font color="Green">E19</font></i></a>, <a class="txt" href="unialg_2.html#E1:25_2"><i><font color="Green">E21</font></i></a>, <a class="ref" href="unialg_2.html#D7" target="_self">Def7</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:25"/>
the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E7:25"><i><font color="Green">E19</font></i></a>, <a class="ref" href="finseq_1.html#T17">FINSEQ_1:17</a></i>;<br/>

<b>thus </b><a NAME="E11:25"/>
<font color="Maroon">c<sub>6</sub></font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a>
 <b>by </b><i><a class="txt" href="unialg_2.html#E8:25"><i><font color="Green">E20</font></i></a></i>;<br/>


</div>
