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<b>let </b><font color="Maroon">c<sub>1</sub></font> be    <a href="struct_0.html#L1">1-sorted</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be    <a href="polyalg1.html#L1" target="_self">AlgebraStr</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:34"/><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is    <a href="polyalg1.html#M1" target="_self">Subalgebra</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E2:34"/><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is    <a href="polyalg1.html#M1" target="_self">Subalgebra</a> of <font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<a NAME="E3:34"/><i><font color="Green">E19</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>
 
<b>by </b><i><a class="txt" href="polyalg1.html#E1:34"><i><font color="Green">E17</font></i></a>, <a class="ref" href="polyalg1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E4:34"/><i><font color="Green">E20</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</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="polyalg1.html#E2:34"><i><font color="Green">E18</font></i></a>, <a class="ref" href="polyalg1.html#D3" target="_self">Def3</a></i>;<br/>
<a NAME="E5:34"/><b>then </b><i><font color="Green">E21</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <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>3</sub></font>
 
<b>by </b><i><a class="txt" href="polyalg1.html#E3:34"><i><font color="Green">E19</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>
<a NAME="E6:34"/><i><font color="Green">E22</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="polyalg1.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E7:34"/><i><font color="Green">E23</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="polyalg1.html#T1" target="_self">Th1</a></i>;<br/>
<a NAME="E8:34"/><i><font color="Green">E24</font></i>: 
 <a href="relat_1.html#K1">dom</a> the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="polyalg1.html#T2" target="_self">Th2</a></i>;<br/>
<a NAME="E9:34"/><i><font color="Green">E25</font></i>: 
<span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span> <a href="tarski.html#R1">c=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="txt" href="polyalg1.html#E4:34"><i><font color="Green">E20</font></i></a>, <a class="ref" href="zfmisc_1.html#T119">ZFMISC_1:119</a></i>;<br/>
<i><font color="Green">E26</font></i>: the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font> = 
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>3</sub></font> <a href="realset1.html#K1">||</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="polyalg1.html#E1:34"><i><font color="Green">E17</font></i></a>, <a class="ref" href="polyalg1.html#D3" target="_self">Def3</a></i>
<br/>.= 
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="polyalg1.html#E5:34"><i><font color="Green">E21</font></i></a>, <a class="txt" href="polyalg1.html#E6:34"><i><font color="Green">E22</font></i></a>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>
;<br/>
<i><font color="Green">E27</font></i>: the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> = 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>3</sub></font> <a href="realset1.html#K1">||</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="polyalg1.html#E1:34"><i><font color="Green">E17</font></i></a>, <a class="ref" href="polyalg1.html#D3" target="_self">Def3</a></i>
<br/>.= 
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="polyalg1.html#E5:34"><i><font color="Green">E21</font></i></a>, <a class="txt" href="polyalg1.html#E7:34"><i><font color="Green">E23</font></i></a>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>
;<br/>
<i><font color="Green">E28</font></i>: the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">c<sub>2</sub></font> = 
the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">c<sub>3</sub></font> <a href="relat_1.html#K7">|</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
<b>by </b><i><a class="txt" href="polyalg1.html#E1:34"><i><font color="Green">E17</font></i></a>, <a class="ref" href="polyalg1.html#D3" target="_self">Def3</a></i>
<br/>.= 
the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="polyalg1.html#E8:34"><i><font color="Green">E24</font></i></a>, <a class="txt" href="polyalg1.html#E9:34"><i><font color="Green">E25</font></i></a>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>
;<br/>
<i><font color="Green">E29</font></i>: the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>2</sub></font> = 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>2</sub></font>

<br/>.= 
 <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="polyalg1.html#E1:34"><i><font color="Green">E17</font></i></a>, <a class="ref" href="polyalg1.html#D3" target="_self">Def3</a></i>
<br/>.= 
the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>3</sub></font>

;<br/>
the <a href="vectsp_1.html#U1">unity</a> of <font color="Maroon">c<sub>2</sub></font> = 
 <a href="vectsp_1.html#K2">1_</a> <font color="Maroon">c<sub>2</sub></font>

<br/>.= 
 <a href="vectsp_1.html#K2">1_</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="polyalg1.html#E1:34"><i><font color="Green">E17</font></i></a>, <a class="ref" href="polyalg1.html#D3" target="_self">Def3</a></i>
<br/>.= 
the <a href="vectsp_1.html#U1">unity</a> of <font color="Maroon">c<sub>3</sub></font>

;<br/>
<b>hence </b><a NAME="E15:34"/>
 <a href="polyalg1.html#G1" target="_self">AlgebraStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="vectsp_1.html#U1">unity</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">c<sub>2</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="polyalg1.html#G1" target="_self">AlgebraStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="vectsp_1.html#U1">unity</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">c<sub>3</sub></font> #)
 <b>by </b><i><a class="txt" href="polyalg1.html#E3:34"><i><font color="Green">E19</font></i></a>, <a class="txt" href="polyalg1.html#E4:34"><i><font color="Green">E20</font></i></a>, <a class="txt" href="polyalg1.html#E10:34"><i><font color="Green">E26</font></i></a>, <a class="txt" href="polyalg1.html#E11:34"><i><font color="Green">E27</font></i></a>, <a class="txt" href="polyalg1.html#E12:34"><i><font color="Green">E28</font></i></a>, <a class="txt" href="polyalg1.html#E13:34"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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