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<b>let </b><font color="Maroon" title="c1">z</font> be  <a href="quaterni.html#V1" title="QUATERNI:attr.1">quaternion</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">z</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> implies <font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span> )</span><br/>

<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E3">A1</font></i>: 
<font color="Maroon" title="c1">z</font> is   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span></span><br/>

<b>then reconsider </b><font color="Maroon" title="c2">x</font> = <font color="Maroon" title="c1">z</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> ;<br/>
<a NAME="E3:6"/><i><font color="Green" title="E4">a</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="6_1"><b>proof </b></a><div class="add">

<a NAME="E1:6_1"/><i><font color="Green" title="E5">B2</font></i>: 
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">x</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span>
 
<b>by </b><i><a class="ref" href="arytm_0.html#D7" title="ARYTM_0:def.7">ARYTM_0:def 7</a></i>;<br/>
<a NAME="E2:6_1"/>
<span class="p1"><a href="arytm_0.html#K5" title="ARYTM_0:func.5">[*</a><span class="default"><font color="Maroon" title="c2">x</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="arytm_0.html#K5" title="ARYTM_0:func.5">*]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><font color="Maroon" title="c2">x</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
 
<b>by </b><i><a class="ref" href="quaterni.html#D6" title="QUATERNI:def.6">QUATERNI:def 6</a></i>;<br/>
<b>hence </b><a NAME="E3:6_1"/>
<font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font>
 <b>by </b><i><a class="txt" href="#E1:6_1"><i><font color="Green" title="E5">B2</font></i></a>, <a class="ref" href="quaterni.html#T23" title="QUATERNI:th.23">QUATERNI:23</a></i>; <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>
<font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a>  = 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><span class="p2">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a> </span>)</span></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="ref" href="quaterni.html#T24" title="QUATERNI:th.24">QUATERNI:24</a></i>
<br/>.= 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a> </span>)</span></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="ref" href="quaterni.html#T33" title="QUATERNI:th.33">QUATERNI:33</a>, <a class="txt" href="#E1:6"><i><font color="Green" title="E3">A1</font></i></a></i>
<br/>.= 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c2">x</font>,<span class="p2">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a> </span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a> </span>)</span></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="ref" href="quaterni.html#T33" title="QUATERNI:th.33">QUATERNI:33</a></i>
<br/>.= 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<font color="Maroon" title="c2">x</font>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a> </span>)</span></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="ref" href="quaterni.html#T33" title="QUATERNI:th.33">QUATERNI:33</a></i>
<br/>.= 
<span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<b>by </b><i><a class="txt" href="#E3:6"><i><font color="Green" title="E4">a</font></i></a>, <a class="ref" href="quaterni.html#T33" title="QUATERNI:th.33">QUATERNI:33</a></i>
;<br/>
<b>hence </b><a NAME="E5:6"/>
<font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <a href="quatern2.html#K4" title="QUATERN2:func.4">&lt;i&gt;</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="quaterni.html#K6" title="QUATERNI:func.6">[*</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<span class="p2">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z</font></span>)</span>,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="numbers.html#K6" title="NUMBERS:func.6">0</a> </span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
