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<a NAME="E1:15_1_1"/>
 ex <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font>, <font color="Olive" title="b3">m</font>, <font color="Olive" title="b4">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>for <font color="Olive" title="b5">x</font>, <font color="Olive" title="b6">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  holds   <a href="bcialg_5.html#K1" title="BCIALG_5:func.1">Polynom</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>,<font color="Olive" title="b5">x</font>,<font color="Olive" title="b6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bcialg_5.html#K1" title="BCIALG_5:func.1">Polynom</a> <font color="Olive" title="b3">m</font>,<font color="Olive" title="b4">n</font>,<font color="Olive" title="b6">y</font>,<font color="Olive" title="b5">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="15_1_1_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon" title="c1">i1</font>, <font color="Maroon" title="c2">j1</font>, <font color="Maroon" title="c3">m1</font>, <font color="Maroon" title="c4">n1</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/>
<a NAME="E2:15_1_1_1"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  holds   <a href="bcialg_5.html#K1" title="BCIALG_5:func.1">Polynom</a> <font color="Maroon" title="c1">i1</font>,<font color="Maroon" title="c2">j1</font>,<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bcialg_5.html#K1" title="BCIALG_5:func.1">Polynom</a> <font color="Maroon" title="c3">m1</font>,<font color="Maroon" title="c4">n1</font>,<font color="Olive" title="b2">y</font>,<font color="Olive" title="b1">x</font>
 
<b>by </b><i><a class="ref" href="struct_0.html#D10" title="STRUCT_0:def.10">STRUCT_0:def 10</a></i>;<br/>
<b>hence </b><a NAME="E3:15_1_1_1"/>
 ex <font color="Olive" title="b1">i</font>, <font color="Olive" title="b2">j</font>, <font color="Olive" title="b3">m</font>, <font color="Olive" title="b4">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  st <br/>for <font color="Olive" title="b5">x</font>, <font color="Olive" title="b6">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  holds   <a href="bcialg_5.html#K1" title="BCIALG_5:func.1">Polynom</a> <font color="Olive" title="b1">i</font>,<font color="Olive" title="b2">j</font>,<font color="Olive" title="b5">x</font>,<font color="Olive" title="b6">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bcialg_5.html#K1" title="BCIALG_5:func.1">Polynom</a> <font color="Olive" title="b3">m</font>,<font color="Olive" title="b4">n</font>,<font color="Olive" title="b6">y</font>,<font color="Olive" title="b5">x</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:15_1_1"/>
 <a href="bcialg_1.html#K3" title="BCIALG_1:func.3">BCI-EXAMPLE</a>  is <a href="bcialg_5.html#V1" title="BCIALG_5:attr.1">quasi-commutative</a>
 <b>by </b><i><a class="ref" href="bcialg_5.html#D2" target="_self" title="BCIALG_5:def.2">Def1</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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