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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">z</font>, <font color="Olive" title="b2">x</font>, <font color="Olive" title="b3">y</font> being  <a href="vectsp_1.html#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">SF</font>  st <font color="Olive" title="b1">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">SF</font> holds <br/>( <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Olive" title="b1">z</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Olive" title="b1">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b3">y</font></span>)</span> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Olive" title="b1">z</font> &amp; <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Olive" title="b1">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="b3">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Olive" title="b1">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="rlvect_1.html#K4" title="RLVECT_1:func.4">-</a> <font color="Olive" title="b3">y</font></span>)</span> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Olive" title="b1">z</font> )</span><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#NM4" title="VECTSP_1:NM.4">Scalar</a> of <font color="Maroon" title="c1">SF</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">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#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</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#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</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#K1" title="VECTSP_2:func.1">/</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#K1" title="VECTSP_2:func.1">/</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#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">z</font> ) )</span><br/>







<a NAME="E1:34"/>
( <font color="Maroon" title="c2">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">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#K1" title="VECTSP_2:func.1">/</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#K1" title="VECTSP_2:func.1">/</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#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">z</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:34_1"/>
<font color="Maroon" title="c2">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">SF</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</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#K1" title="VECTSP_2:func.1">/</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#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">z</font></span><br/>

<b>hence </b><span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</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#K1" title="VECTSP_2:func.1">/</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#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">z</font></span>)</span>
<b>by </b><i><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#K4" title="RLVECT_1:func.4">-</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">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 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="E2:34"/>
( <font color="Maroon" title="c2">z</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">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#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">z</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</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#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c4">y</font></span>)</span> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</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#K1" title="VECTSP_2:func.1">/</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#K1" title="VECTSP_2:func.1">/</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#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">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>; <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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