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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><a NAME="E1:35"/><i><font color="Green">E18</font></i>: 
 <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> #)
 ;<br/>

<a NAME="E2:35"/><i><font color="Green">E19</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="E3:35"/><i><font color="Green">E20</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="E4:35"/><i><font color="Green">E21</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/>
<b>thus </b><a NAME="E5:35"/>
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#E1:35"><i><font color="Green">E18</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="polyalg1.html#D3" target="_self">POLYALG1:def 3</a><br/>

<b>thus </b> <a href="vectsp_1.html#K2">1_</a> <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>

<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#E1:35"><i><font color="Green">E18</font></i></a></i>
;<br/>

<b>thus </b> <a href="rlvect_1.html#K1">0.</a> <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>

<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#E1:35"><i><font color="Green">E18</font></i></a></i>
;<br/>

<b>thus </b><a NAME="E8:35"/>
the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 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#E1:35"><i><font color="Green">E18</font></i></a>, <a class="txt" href="polyalg1.html#E2:35"><i><font color="Green">E19</font></i></a>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>;<br/>

<b>thus </b><a NAME="E9:35"/>
the <a href="group_1.html#U1">mult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 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#E1:35"><i><font color="Green">E18</font></i></a>, <a class="txt" href="polyalg1.html#E3:35"><i><font color="Green">E20</font></i></a>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>;<br/>

<b>thus </b><a NAME="E10:35"/>
the <a href="vectsp_1.html#U2">lmult</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> 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#E1:35"><i><font color="Green">E18</font></i></a>, <a class="txt" href="polyalg1.html#E4:35"><i><font color="Green">E21</font></i></a>, <a class="ref" href="relat_1.html#T97">RELAT_1:97</a></i>;<br/>


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