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<span class="kw">let </span><font color="Maroon" title="c1">z1</font>, <font color="Maroon" title="c2">z2</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"> (  <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</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="c2">z2</font> &amp;  <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c2">z2</font> &amp;  <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c2">z2</font> &amp;  <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c2">z2</font> implies <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z2</font> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:52"/><span class="lab"><font color="Green" title="E33">A1</font></span>: 
 <a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</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="c2">z2</font>
 <span class="kw">and </span><br/><a NAME="E2:52"/><span class="lab"><font color="Green" title="E34">A2</font></span>: 
 <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c2">z2</font>
 <span class="kw">and </span><br/><a NAME="E3:52"/><span class="lab"><font color="Green" title="E35">A3</font></span>: 
 <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c2">z2</font>
 <span class="kw">and </span><br/><a NAME="E4:52"/><span class="lab"><font color="Green" title="E36">A4</font></span>: 
 <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c2">z2</font>
 ; <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">z1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z2</font></span><br/>

<span class="kw">thus </span><font color="Maroon" title="c1">z1</font> = 
<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> <font color="Maroon" title="c2">z2</font></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c2">z2</font></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c2">z2</font></span>)</span>,<span class="p2">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c2">z2</font></span>)</span></span><a href="quaterni.html#K6" title="QUATERNI:func.6">*]</a></span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E33">A1</font></span></a>, <a class="txt" href="#E2:52"><span class="lab"><font color="Green" title="E34">A2</font></span></a>, <a class="txt" href="#E3:52"><span class="lab"><font color="Green" title="E35">A3</font></span></a>, <a class="txt" href="#E4:52"><span class="lab"><font color="Green" title="E36">A4</font></span></a>, <a class="ref" href="quaterni.html#T24" target="_self" title="QUATERNI:th.24">Th24</a></span>
<br/>.= 
<font color="Maroon" title="c2">z2</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="quaterni.html#T24" target="_self" title="QUATERNI:th.24">Th24</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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