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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">z</font>, <font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">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/>







<a NAME="E1:39"/><i><font color="Green" title="E21">A1</font></i>: 
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font>, <font color="Olive" title="b3">z</font> being  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Scalar</a> of <font color="Maroon" title="c1">SF</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Olive" title="b3">z</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">y</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Olive" title="b3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Olive" title="b3">z</font>
 
<b>by </b><i><a class="ref" href="vectsp_1.html#D18" title="VECTSP_1:def.18">VECTSP_1:def 18</a></i>;<br/>
<a NAME="E2:39"/>
( <font color="Maroon" title="c2">z</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> implies <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="39_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:39_1"/><i><font color="Green" title="E22">A2</font></i>: 
<font color="Maroon" title="c2">z</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>
 ;<br/>

<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="rlvect_1.html#K5" title="RLVECT_1:func.5">-</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font></span>)</span>
<b>by </b><i><a class="txt" href="vectsp_2.html#E1:39_1"><i><font color="Green" title="E22">A2</font></i></a>, <a class="ref" href="vectsp_2.html#T54" target="_self" title="VECTSP_2:th.54">Th54</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font>
<b>by </b><i><a class="txt" href="vectsp_2.html#E1:39"><i><font color="Green" title="E21">A1</font></i></a></i>
;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E3:39"/>
( <font color="Maroon" title="c2">z</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> implies ( <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">+</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="rlvect_1.html#K6" title="RLVECT_1:func.6">-</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="vectsp_2.html#K2" title="VECTSP_2:func.2">/</a> <font color="Maroon" title="c2">z</font> ) )
 <b>by </b><i><a class="txt" href="vectsp_2.html#E1:39"><i><font color="Green" title="E21">A1</font></i></a></i>;<br/>


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