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<b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">j</font></span>)</span> <a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|-&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="rvsum_1.html#K22" title="RVSUM_1:func.22">|-&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="rvsum_1.html#K22" title="RVSUM_1:func.22">|-&gt;</a> <font color="Olive" title="b1">z</font></span>)</span></span>)</span></span><br/><b>let </b><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:()"><i><font color="Red">::  thesis: </font></i></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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">j</font></span>)</span> <a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|-&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="rvsum_1.html#K22" title="RVSUM_1:func.22">|-&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="rvsum_1.html#K22" title="RVSUM_1:func.22">|-&gt;</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span></span><br/>





<b>thus </b> <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="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c2">j</font></span>)</span> <a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|-&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">$$</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|-&gt;</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><a href="binop_2.html#K29" title="BINOP_2:func.29">multcomplex</a>  <a href="finsop_1.html#K2" title="FINSOP_1:func.2">$$</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="rvsum_1.html#K22" title="RVSUM_1:func.22">|-&gt;</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="setwop_2.html#T37" title="SETWOP_2:th.37">SETWOP_2:37</a></i>
<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="rvsum_1.html#K22" title="RVSUM_1:func.22">|-&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="rvsum_1.html#K22" title="RVSUM_1:func.22">|-&gt;</a> <font color="Maroon" title="c3">z</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="binop_2.html#D5" title="BINOP_2:def.5">BINOP_2:def 5</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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