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<span class="kw">let </span><font color="Maroon" title="c1">z</font>, <font color="Maroon" title="c2">z1</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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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> <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c1">z</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:11"/><span class="lab"><font color="Green" title="E4">A1</font></span>: 
<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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c1">z</font></span><br/>

<a NAME="E2:11"/><span class="lab"><font color="Green" title="E5">A2</font></span>: 
 <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="quatern3.html#E3"><span class="lab"><font color="Green" title="E3">Lm2</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c3">x</font> = <font color="Maroon" title="c1">z</font> as   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a></span>;<br/>
<a NAME="E4:11"/><span class="lab"><font color="Green" title="E6">A3</font></span>: 
(  <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  &amp;  <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:11"><span class="lab"><font color="Green" title="E4">A1</font></span></a>, <a class="txt" href="quatern3.html#E3"><span class="lab"><font color="Green" title="E3">Lm2</font></span></a></span>;<br/>
<span class="kw">thus </span><a NAME="E5:11"/>
<font color="Maroon" title="c1">z</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c2">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z1</font> <a href="quaterni.html#K27" title="QUATERNI:func.27">*</a> <font color="Maroon" title="c1">z</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:11"><span class="lab"><font color="Green" title="E6">A3</font></span></a>, <a class="txt" href="#E2:11"><span class="lab"><font color="Green" title="E5">A2</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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