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<b>let </b><font color="Maroon" title="c1">SF</font> be   <a href="vectsp_2.html#NM3" title="VECTSP_2:NM.3">Skew-Field</a>;<br/><b>let </b><font color="Maroon" title="c2">x</font>, <font color="Maroon" title="c3">y</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Scalar</a> of <font color="Maroon" title="c1">SF</font>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>now </b></a><div class="add"><a NAME="E1:30_1"/><i><font color="Green" title="E15">A1</font></i>: 
( <font color="Maroon" title="c2">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font> implies <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">"</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:30_1_1"/><i><font color="Green" title="E16">A2</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font>
 ;<br/>

<a NAME="E2:30_1_1"/><b>then </b><i><font color="Green" title="E17">A3</font></i>: 
<font color="Maroon" title="c3">y</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">SF</font>
 
<b>by </b><i><a class="ref" href="vectsp_2.html#T39" target="_self" title="VECTSP_2:th.39">Th39</a></i>;<br/>
<a NAME="E3:30_1_1"/>
<font color="Maroon" title="c3">y</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font>
 
<b>by </b><i><a class="txt" href="vectsp_2.html#E1:30_1_1"><i><font color="Green" title="E16">A2</font></i></a>, <a class="ref" href="vectsp_2.html#T41" target="_self" title="VECTSP_2:th.41">Th41</a></i>;<br/>
<b>hence </b><a NAME="E4:30_1_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">"</a> 
 <b>by </b><i><a class="txt" href="vectsp_2.html#E2:30_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="ref" href="vectsp_2.html#D7" target="_self" title="VECTSP_2:def.7">Def7</a></i>;<br/>


</div><b>end;</b></div><a NAME="E2:30_1"/>
( <font color="Maroon" title="c2">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font> implies <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">"</a>  )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:30_1_2"/><i><font color="Green" title="E16">A4</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font>
 ;<br/>

<a NAME="E2:30_1_2"/><b>then </b>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">0.</a> <font color="Maroon" title="c1">SF</font>
 
<b>by </b><i><a class="ref" href="vectsp_2.html#T39" target="_self" title="VECTSP_2:th.39">Th39</a></i>;<br/>
<b>hence </b><a NAME="E3:30_1_2"/>
<font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">"</a> 
 <b>by </b><i><a class="txt" href="vectsp_2.html#E1:30_1_2"><i><font color="Green" title="E16">A4</font></i></a>, <a class="ref" href="vectsp_2.html#D7" target="_self" title="VECTSP_2:def.7">Def7</a></i>;<br/>


</div><b>end;</b></div><b>hence </b><a NAME="E3:30_1"/>
( <font color="Maroon" title="c2">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font> implies ( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">"</a>  &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">"</a>  ) )
 <b>by </b><i><a class="txt" href="vectsp_2.html#E1:30_1"><i><font color="Green" title="E15">A1</font></i></a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:30"/>
( <font color="Maroon" title="c2">x</font> <a href="group_1.html#K1" title="GROUP_1:func.1">*</a> <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K2" title="GROUP_1:func.2">1.</a> <font color="Maroon" title="c1">SF</font> implies ( <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">"</a>  &amp; <font color="Maroon" title="c3">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">"</a>  ) )
 ;<br/>


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