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<b>let </b><font color="Maroon" title="c1">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">z</font> being   <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="complsp1.html#K8" title="COMPLSP1:func.8">COMPLEX</a> <font color="Maroon" title="c1">n</font> holds  <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  <a href="complsp1.html#K14" title="COMPLSP1:func.14">*</a> <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <font color="Maroon" title="c1">n</font></span><br/><b>let </b><font color="Maroon" title="c2">z</font> be    <a href="finseq_2.html#M2" title="FINSEQ_2:mode.2">Element</a> of  <a href="complsp1.html#K8" title="COMPLSP1:func.8">COMPLEX</a> <font color="Maroon" title="c1">n</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  <a href="complsp1.html#K14" title="COMPLSP1:func.14">*</a> <font color="Maroon" title="c2">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <font color="Maroon" title="c1">n</font></span><br/>



<a NAME="E1:45"/><i><font color="Green" title="E24">A1</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c2">z</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> 
 
;<br/>
<b>thus </b><a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a>  <a href="complsp1.html#K14" title="COMPLSP1:func.14">*</a> <font color="Maroon" title="c2">z</font> = 
<a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="finseqop.html#K3" title="FINSEQOP:func.3">[;]</a> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> ,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> </span>)</span> <a href="finseqop.html#K5" title="FINSEQOP:func.5">*</a> <font color="Maroon" title="c2">z</font></span>)</span>
<b>by </b><i><a class="ref" href="funcop_1.html#T44" title="FUNCOP_1:th.44">FUNCOP_1:44</a></i>
<br/>.= 
<a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="finseqop.html#K3" title="FINSEQOP:func.3">[;]</a> <a href="complex1.html#K5" title="COMPLEX1:func.5">0c</a> ,<font color="Maroon" title="c2">z</font>
<b>by </b><i><a class="txt" href="complsp1.html#E1:45"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="relat_1.html#T79" title="RELAT_1:th.79">RELAT_1:79</a></i>
<br/>.= 
 <a href="complsp1.html#K11" title="COMPLSP1:func.11">0c</a> <font color="Maroon" title="c1">n</font>
<b>by </b><i><a class="ref" href="complsp1.html#T7" target="_self" title="COMPLSP1:th.7">Th7</a>, <a class="ref" href="complsp1.html#T15" target="_self" title="COMPLSP1:th.15">Th15</a>, <a class="ref" href="binop_2.html#T1" title="BINOP_2:th.1">BINOP_2:1</a>, <a class="ref" href="finseqop.html#T80" title="FINSEQOP:th.80">FINSEQOP:80</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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