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<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:44_3_1_1"/>
( <font color="Maroon" title="c1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  or  not <font color="Maroon" title="c1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_1_1_1"><b>suppose </b></a><a NAME="E1:44_3_1_1_1"/>
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="quaterni.html#K15" title="QUATERNI:func.15">Im2</a> <font color="Maroon" title="c1">z</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a></span><br/><div class="add"><b>hence </b><a NAME="E2:44_3_1_1_1"/>
 <a href="quaterni.html#K15" title="QUATERNI:func.15">Im2</a> <font color="Maroon" title="c1">z</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>
 <b>by </b><i><a class="ref" href="quaterni.html#D15" target="_self" title="QUATERNI:def.15">Def15</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="44_3_1_1_2"><b>suppose </b></a><a NAME="E1:44_3_1_1_2"/>
not <font color="Maroon" title="c1">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="quaterni.html#K15" title="QUATERNI:func.15">Im2</a> <font color="Maroon" title="c1">z</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a></span><br/><div class="add"><b>then consider </b><font color="Maroon" title="c2">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of 4, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> <b> such that </b><br/><a NAME="E3:44_3_1_1_2"/>
<font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font>
 <b>and </b><br/><a NAME="E4:44_3_1_1_2"/><i><font color="Green" title="E25">A5</font></i>: 
 <a href="quaterni.html#K15" title="QUATERNI:func.15">Im2</a> <font color="Maroon" title="c1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">f</font> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> 2
 <b>by </b><i><a class="ref" href="quaterni.html#D15" target="_self" title="QUATERNI:def.15">Def15</a></i>;<br/><b>thus </b><a NAME="E5:44_3_1_1_2"/>
 <a href="quaterni.html#K15" title="QUATERNI:func.15">Im2</a> <font color="Maroon" title="c1">z</font> is <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>
 <b>by </b><i><a class="txt" href="quaterni.html#E4:44_3_1_1_2"><i><font color="Green" title="E25">A5</font></i></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></div><b>end;</b></div>

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