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<span class="kw">let </span><font color="Maroon" title="c1">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="complfld.html#K1" title="COMPLFLD:func.1">F_Complex</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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>, <font color="Olive" title="b2">w</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="algnum_1.html#K7" title="ALGNUM_1:func.7">FQ</a> <font color="Maroon" title="c1">x</font> holds  <span class="p1">(<span class="default"><a href="algnum_1.html#K9" title="ALGNUM_1:func.9">FQ_mult</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">z</font>,<font color="Olive" title="b2">w</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b2">w</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">z</font>, <font color="Maroon" title="c3">w</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="algnum_1.html#K7" title="ALGNUM_1:func.7">FQ</a> <font color="Maroon" title="c1">x</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="algnum_1.html#K9" title="ALGNUM_1:func.9">FQ_mult</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">w</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">w</font></span><br/>



<span class="kw">thus </span><span class="p1">(<span class="default"><a href="algnum_1.html#K9" title="ALGNUM_1:func.9">FQ_mult</a> <font color="Maroon" title="c1">x</font></span>)</span> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">w</font>) = 
<a href="binop_2.html#K5" title="BINOP_2:func.5">multcomplex</a> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">z</font>,<font color="Maroon" title="c3">w</font>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T49" onmouseover="rs('funct_1/T49')" onmouseout="rh()">FUNCT_1:49</a>, <a class="ref" href="zfmisc_1.html#T87" onmouseover="rs('zfmisc_1/T87')" onmouseout="rh()">ZFMISC_1:87</a></span>
<br/>.= 
<font color="Maroon" title="c2">z</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c3">w</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="binop_2.html#D5" onmouseover="rs('binop_2/D5')" onmouseout="rh()">BINOP_2:def 5</a></span>
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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