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<span class="kw">let </span><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">z</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>  holds   <a href="rvsum_1.html#K20" title="RVSUM_1:func.20">Product</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <font color="Maroon" title="c2">j</font></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Olive" title="b1">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K20" title="RVSUM_1:func.20">Product</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Olive" title="b1">z</font></span>)</span></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K20" title="RVSUM_1:func.20">Product</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Olive" title="b1">z</font></span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c3">z</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="rvsum_1.html#K20" title="RVSUM_1:func.20">Product</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <font color="Maroon" title="c2">j</font></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">z</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K20" title="RVSUM_1:func.20">Product</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K20" title="RVSUM_1:func.20">Product</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span></span><br/>





<span class="kw">thus </span> <a href="rvsum_1.html#K20" title="RVSUM_1:func.20">Product</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> <font color="Maroon" title="c2">j</font></span>)</span> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">z</font></span>)</span> = 
<a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<span class="p1">(<span class="default"><a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a> <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="setwop_2.html#T26" title="SETWOP_2:th.26">SETWOP_2:26</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="rvsum_1.html#K20" title="RVSUM_1:func.20">Product</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span> <a href="binop_2.html#K5" title="BINOP_2:func.5">*</a> <span class="p1">(<span class="default"><a href="rvsum_1.html#K20" title="RVSUM_1:func.20">Product</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="finseqop.html#K4" title="FINSEQOP:func.4">|-&gt;</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binop_2.html#D5" title="BINOP_2:def.5">BINOP_2:def 5</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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