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<b>let </b><font color="Maroon">W1</font> be  <a href="unialg_1.html#V3">strict</a>  <a href="unialg_2.html#M3" target="_self">SubAlgebra</a> of <font color="Maroon">U0</font>, <font color="Maroon">W2</font> be  <a href="unialg_1.html#V3">strict</a>  <a href="unialg_2.html#M3" target="_self">SubAlgebra</a> of <font color="Maroon">U0</font>;<br/>

<b>assume </b><a NAME="E1:30_1_2"/><i><font color="Green">E55</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U2</font> &amp; ( for <font color="Olive">B1</font> being non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font>  st <font color="Olive">B1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W1</font> holds <br/>( the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">W1</font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">U0</font>,<font color="Olive">B1</font> &amp; <font color="Olive">B1</font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a> ) ) &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U2</font> &amp; ( for <font color="Olive">B2</font> being non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font>  st <font color="Olive">B2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">W2</font> holds <br/>( the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">U0</font>,<font color="Olive">B2</font> &amp; <font color="Olive">B2</font> is <a href="unialg_2.html#V1" target="_self">opers_closed</a> ) ) )
 ;<br/>

<a NAME="E2:30_1_2"/><i><font color="Green">E56</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U2</font> is   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font> )
 
<b>by </b><i/>;<br/>
<a NAME="E3:30_1_2"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U2</font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U2</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">C</font> = the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U1</font> <a href="xboole_0.html#K3">/\</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">U2</font> as  non <a href="xboole_0.html#V1">empty</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">U0</font> <b>by </b><i>, , <a class="ref" href="xboole_0.html#D7">XBOOLE_0:def 7</a>, <a class="ref" href="xboole_1.html#T1">XBOOLE_1:1</a></i>;<br/>
<a NAME="E5:30_1_2"/>
the <a href="unialg_1.html#U1">charact</a> of <font color="Maroon">W2</font> <a href="hidden.html#R1">=</a>  <a href="unialg_2.html#K3" target="_self">Opers</a> <font color="Maroon">U0</font>,<font color="Maroon">C</font>
 
<b>by </b><i><a class="txt" href="unialg_2.html#E1:30"><i><font color="Green">E20</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:30_1_2"/>
<font color="Maroon">W1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">W2</font>
 <b>by </b><i><a class="txt" href="unialg_2.html#E1:30"><i><font color="Green">E20</font></i></a></i>;<br/>


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