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<div class="add">

<b>let </b><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>;<br/>

<b>set </b><font color="Maroon" title="c2">L</font> =  <a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <font color="Maroon" title="c1">K</font>;<br/>
<a NAME="E1:23"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <font color="Maroon" title="c1">K</font></span>)</span> holds  <font color="Olive" title="b1">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Olive" title="b2">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="23_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <span class="p1">(<span class="default"><a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <font color="Maroon" title="c1">K</font></span>)</span>;<br/>

<b>reconsider </b><font color="Maroon" title="c5">a</font> = <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c6">b</font> = <font color="Maroon" title="c4">y</font> as   <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">K</font> ;<br/>
<a NAME="E2:23_1"/>
<font color="Maroon" title="c6">b</font> <a href="group_1.html#K10" title="GROUP_1:func.10">*</a> <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">y</font>
 
<b>by </b><i><a class="txt" href="mod_4.html#E5"><i><font color="Green" title="E4">Lm3</font></i></a></i>;<br/>
<b>hence </b><a NAME="E3:23_1"/>
<font color="Maroon" title="c3">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c3">x</font>
 <b>by </b><i><a class="txt" href="mod_4.html#E5"><i><font color="Green" title="E4">Lm3</font></i></a></i>;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E2:23"/>
 <a href="mod_4.html#K2" title="MOD_4:func.2">opp</a> <font color="Maroon" title="c1">K</font> is  <a href="vectsp_1.html#V3" title="VECTSP_1:attr.3">strict</a> <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>
 <b>by </b><i><a class="ref" href="group_1.html#D16" title="GROUP_1:def.16">GROUP_1:def 16</a></i>;<br/>


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