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<span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">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">A</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font> being    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</a> (<font color="Olive" title="b1">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>) holds  <span class="p1">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K8" title="LPSPACC1:func.8">multcomplexcpfunc</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b2">f</font>)</span>)</span>,<font color="Olive" title="b3">g</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lpspacc1.html#K8" title="LPSPACC1:func.8">multcomplexcpfunc</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Olive" title="b1">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font>)</span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">A</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">f</font>, <font color="Olive" title="b2">g</font> being    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</a> (<font color="Maroon" title="c3">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>) holds  <span class="p1">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K8" title="LPSPACC1:func.8">multcomplexcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Olive" title="b1">f</font>)</span>)</span>,<font color="Olive" title="b2">g</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lpspacc1.html#K8" title="LPSPACC1:func.8">multcomplexcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font>)</span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font> be    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</a> (<font color="Maroon" title="c3">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">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"> <span class="p1">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K8" title="LPSPACC1:func.8">multcomplexcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font>)</span>)</span>,<font color="Maroon" title="c5">g</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lpspacc1.html#K8" title="LPSPACC1:func.8">multcomplexcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span>)</span><br/>







<span class="kw">reconsider </span><font color="Maroon" title="c6">a</font> = <font color="Maroon" title="c2">a</font> as    <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>  <span class="kw">by</span> <span class="lab"><a class="ref" href="xcmplx_0.html#D2" onmouseover="rs('xcmplx_0/D2')" onmouseout="rh()">XCMPLX_0:def 2</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c7">i</font> = <span class="p1">(<span class="default"><a href="lpspacc1.html#K8" title="LPSPACC1:func.8">multcomplexcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c6">a</font>,<font color="Maroon" title="c4">f</font>) as    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</a> (<font color="Maroon" title="c3">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>) ;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">j</font> = <span class="p1">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c9">k</font> = <span class="p1">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c5">g</font>);<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">l</font> = <span class="p1">(<span class="default"><a href="lpspacc1.html#K8" title="LPSPACC1:func.8">multcomplexcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="binop_1.html#K2" title="BINOP_1:func.2">.</a> (<font color="Maroon" title="c6">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span>) as    <a href="rfunct_3.html#M2" title="RFUNCT_3:mode.2">Element</a> of  <a href="rfunct_3.html#K3" title="RFUNCT_3:func.3">PFuncs</a> (<font color="Maroon" title="c3">A</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>) ;<br/>
<a NAME="E4:28"/><span class="lab"><font color="Green" title="E16">A1</font></span>: 
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c7">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c7">i</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">g</font></span>)</span> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#T5" target="_self" onmouseover="rs('lpspacc1/T5')" onmouseout="rh()">Th5</a>, <a class="ref" href="lpspacc1.html#T7" target="_self" onmouseover="rs('lpspacc1/T7')" onmouseout="rh()">Th7</a></span>;<br/>
<a NAME="E5:28"/><span class="lab"><font color="Green" title="E17">A2</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c5">g</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#T5" target="_self" onmouseover="rs('lpspacc1/T5')" onmouseout="rh()">Th5</a></span>;<br/>
<div><span class="lab"><font color="Green" title="E18">A3</font></span>: <a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="28_1"><span class="kw">now </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">  for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">A</font>  st <font color="Olive" title="b1">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> holds <br/><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font></span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c11">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">A</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"> ( <font color="Maroon" title="c11">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> implies <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> )</span><br/><a NAME="E1:28_1"/><span class="lab"><font color="Green" title="E19">A4</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="lpspacc1.html#K3" title="LPSPACC1:func.3">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#D3" target="_self" onmouseover="rs('lpspacc1/D3')" onmouseout="rh()">Def3</a></span>;<br/><span class="kw">assume </span><a NAME="E2:28_1"/><span class="lab"><font color="Green" title="E20">A5</font></span>: 
<font color="Maroon" title="c11">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c5">g</font>)</span>)</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span><br/><a NAME="E3:28_1"/><span class="kw">then </span>
<font color="Maroon" title="c11">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="lpspacc1.html#K3" title="LPSPACC1:func.3">(#)</a> <font color="Maroon" title="c5">g</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="ref" href="valued_1.html#D4" onmouseover="rs('valued_1/D4')" onmouseout="rh()">VALUED_1:def 4</a></span>;<br/><a NAME="E4:28_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E21">A6</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:28_1"><span class="lab"><font color="Green" title="E19">A4</font></span></a>, <a class="ref" href="valued_1.html#D4" onmouseover="rs('valued_1/D4')" onmouseout="rh()">VALUED_1:def 4</a></span>;<br/><a NAME="E5:28_1"/><span class="lab"><font color="Green" title="E22">A7</font></span>: 
( <font color="Maroon" title="c7">i</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="lpspacc1.html#K5" title="LPSPACC1:func.5">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> &amp;  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="lpspacc1.html#K5" title="LPSPACC1:func.5">(#)</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#D4" target="_self" onmouseover="rs('lpspacc1/D4')" onmouseout="rh()">Def4</a>, <a class="ref" href="valued_1.html#D5" onmouseover="rs('valued_1/D5')" onmouseout="rh()">VALUED_1:def 5</a></span>;<br/><a NAME="E6:28_1"/>
<font color="Maroon" title="c11">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c4">f</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E2:28_1"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="ref" href="xboole_0.html#D4" onmouseover="rs('xboole_0/D4')" onmouseout="rh()">XBOOLE_0:def 4</a></span>;<br/><a NAME="E7:28_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A8</font></span>: 
<font color="Maroon" title="c7">i</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:28_1"><span class="lab"><font color="Green" title="E22">A7</font></span></a>, <a class="ref" href="valued_1.html#D5" onmouseover="rs('valued_1/D5')" onmouseout="rh()">VALUED_1:def 5</a></span>;<br/><a NAME="E8:28_1"/><span class="lab"><font color="Green" title="E24">A9</font></span>: 
<font color="Maroon" title="c10">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="lpspacc1.html#K5" title="LPSPACC1:func.5">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#D4" target="_self" onmouseover="rs('lpspacc1/D4')" onmouseout="rh()">Def4</a></span>;<br/><a NAME="E9:28_1"/>
<font color="Maroon" title="c11">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">a</font> <a href="lpspacc1.html#K5" title="LPSPACC1:func.5">(#)</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E5:28"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E2:28_1"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="ref" href="valued_1.html#D5" onmouseover="rs('valued_1/D5')" onmouseout="rh()">VALUED_1:def 5</a></span>;<br/><a NAME="E10:28_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E25">A10</font></span>: 
<font color="Maroon" title="c10">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28_1"><span class="lab"><font color="Green" title="E21">A6</font></span></a>, <a class="txt" href="#E8:28_1"><span class="lab"><font color="Green" title="E24">A9</font></span></a>, <a class="ref" href="valued_1.html#D5" onmouseover="rs('valued_1/D5')" onmouseout="rh()">VALUED_1:def 5</a></span>;<br/><a NAME="E11:28_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">i</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">g</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:28_1"><span class="lab"><font color="Green" title="E20">A5</font></span></a>, <a class="ref" href="lpspacc1.html#T5" target="_self" onmouseover="rs('lpspacc1/T5')" onmouseout="rh()">Th5</a></span>;<br/><span class="kw">hence </span><a NAME="E12:28_1"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c7">i</font>,<font color="Maroon" title="c5">g</font>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">l</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:28_1"><span class="lab"><font color="Green" title="E23">A8</font></span></a>, <a class="txt" href="#E10:28_1"><span class="lab"><font color="Green" title="E25">A10</font></span></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/></div><span class="kw">end;</span></div>
<a NAME="E7:28"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c10">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="lpspacc1.html#T7" target="_self" onmouseover="rs('lpspacc1/T7')" onmouseout="rh()">Th7</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:28"/>
<span class="p1">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K8" title="LPSPACC1:func.8">multcomplexcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">a</font>,<font color="Maroon" title="c4">f</font>)</span>)</span>,<font color="Maroon" title="c5">g</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="lpspacc1.html#K8" title="LPSPACC1:func.8">multcomplexcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Maroon" title="c2">a</font>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="lpspacc1.html#K7" title="LPSPACC1:func.7">multcpfunc</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="lpspace1.html#K2" title="LPSPACE1:func.2">.</a> (<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font>)</span>)</span>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:28"><span class="lab"><font color="Green" title="E16">A1</font></span></a>, <a class="txt" href="#E5:28"><span class="lab"><font color="Green" title="E17">A2</font></span></a>, <a class="txt" href="#E6:28"><span class="lab"><font color="Green" title="E18">A3</font></span></a>, <a class="ref" href="partfun1.html#T5" onmouseover="rs('partfun1/T5')" onmouseout="rh()">PARTFUN1:5</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/>


</div>
