<?xml version="1.0"?>
<div class="add">

<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">y</font>, <font color="Olive" title="b2">z</font>, <font color="Olive" title="b3">x</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">y</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> &amp; <font color="Olive" title="b2">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/><font color="Olive" title="b3">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Olive" title="b2">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Olive" title="b2">z</font></span>)</span> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Olive" title="b1">y</font></span><br/><b>let </b><font color="Maroon" title="c2">y</font>, <font color="Maroon" title="c3">z</font>, <font color="Maroon" title="c4">x</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">y</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> &amp; <font color="Maroon" title="c3">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 <font color="Maroon" title="c4">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">y</font> )</span><br/>







<b>assume </b><a NAME="E1:35"/><i><font color="Green" title="E18">A1</font></i>: 
<font color="Maroon" title="c2">y</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"> (  not <font color="Maroon" title="c3">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> or <font color="Maroon" title="c4">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">y</font> )</span><br/>

<b>assume </b><a NAME="E2:35"/><i><font color="Green" title="E19">A2</font></i>: 
<font color="Maroon" title="c3">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"> <font color="Maroon" title="c4">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">y</font></span><br/>

<a NAME="E3:35"/><b>then </b>
<font color="Maroon" title="c3">z</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a>  <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>
 
<b>by </b><i><a class="ref" href="vectsp_2.html#T48" target="_self" title="VECTSP_2:th.48">Th48</a></i>;<br/>
<b>hence </b><font color="Maroon" title="c4">x</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c3">z</font></span>)</span> = 
<font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E1:35"><i><font color="Green" title="E18">A1</font></i></a>, <a class="ref" href="vectsp_2.html#T46" target="_self" title="VECTSP_2:th.46">Th46</a></i>
<br/>.= 
<font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">y</font> <a href="algstr_0.html#K11" title="ALGSTR_0:func.11">"</a> </span>)</span></span>)</span>
<b>by </b><i><a class="txt" href="#E2:35"><i><font color="Green" title="E19">A2</font></i></a>, <a class="ref" href="vectsp_2.html#T49" target="_self" title="VECTSP_2:th.49">Th49</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">x</font> <a href="algstr_0.html#K6" title="ALGSTR_0:func.6">*</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="vectsp_2.html#K1" title="VECTSP_2:func.1">/</a> <font color="Maroon" title="c2">y</font>
<b>by </b><i><a class="ref" href="group_1.html#D4" title="GROUP_1:def.4">GROUP_1:def 4</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>
