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<font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K9" title="QUATERNI:func.9">-</a> <font color="Maroon" title="c2">z2</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <span class="p5">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K23" title="QUATERNI:func.23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p0">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p5">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p4">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="quaterni.html#D22" target="_self" title="QUATERNI:def.22">Def22</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K23" title="QUATERNI:func.23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <span class="p0">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p5">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p4">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="quaterni.html#T41" target="_self" title="QUATERNI:th.41">Th41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K23" title="QUATERNI:func.23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <span class="p5">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p4">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="quaterni.html#T41" target="_self" title="QUATERNI:th.41">Th41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K23" title="QUATERNI:func.23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p4">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K3" title="REAL_1:func.3">+</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <span class="p4">(<span class="default"><a href="quaterni.html#K28" title="QUATERNI:func.28">-</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="quaterni.html#T41" target="_self" title="QUATERNI:th.41">Th41</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p4">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K23" title="QUATERNI:func.23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p4">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span>
<b>by </b><i><a class="ref" href="quaterni.html#T41" target="_self" title="QUATERNI:th.41">Th41</a></i>
;<br/>
<b>hence </b><a NAME="E2:85_1_1"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="quaterni.html#K1" title="QUATERNI:func.1">QUATERNION</a>  holds <br/> ( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">z1</font> <a href="quaterni.html#K9" title="QUATERNI:func.9">-</a> <font color="Maroon" title="c2">z2</font> iff <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p4">(<span class="default"><a href="quaterni.html#K17" title="QUATERNI:func.17">Rea</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K23" title="QUATERNI:func.23">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p5">(<span class="default"><a href="quaterni.html#K18" title="QUATERNI:func.18">Im1</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="xcmplx_0.html#K1" title="XCMPLX_0:func.1">&lt;i&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p4">(<span class="default"><a href="quaterni.html#K19" title="QUATERNI:func.19">Im2</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K11" title="QUATERNI:func.11">&lt;j&gt;</a> </span>)</span></span>)</span> <a href="quaterni.html#K26" title="QUATERNI:func.26">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c1">z1</font></span>)</span> <a href="real_1.html#K5" title="REAL_1:func.5">-</a> <span class="p3">(<span class="default"><a href="quaterni.html#K20" title="QUATERNI:func.20">Im3</a> <font color="Maroon" title="c2">z2</font></span>)</span></span>)</span> <a href="quaterni.html#K25" title="QUATERNI:func.25">*</a> <a href="quaterni.html#K12" title="QUATERNI:func.12">&lt;k&gt;</a> </span>)</span> )
 ;<br/>


</div>
