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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</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">a</font> being   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><br/>  for <font color="Olive" title="b2">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="cfuncdom.html#K8" title="CFUNCDOM:func.8">CAlgebra</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font></span>)</span>  st <font color="Olive" title="b2">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cc0sp2.html#K6" title="CC0SP2:func.6">CC_0_Functions</a> <font color="Maroon" title="c1">X</font> holds <br/><font color="Olive" title="b1">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b2">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cc0sp2.html#K6" title="CC0SP2:func.6">CC_0_Functions</a> <font color="Maroon" title="c1">X</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c2">W</font> =  <a href="cc0sp2.html#K6" title="CC0SP2:func.6">CC_0_Functions</a> <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c3">V</font> =  <a href="cfuncdom.html#K8" title="CFUNCDOM:func.8">CAlgebra</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">let </span><font color="Maroon" title="c4">a</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</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">u</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="cfuncdom.html#K8" title="CFUNCDOM:func.8">CAlgebra</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font></span>)</span>  st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cc0sp2.html#K6" title="CC0SP2:func.6">CC_0_Functions</a> <font color="Maroon" title="c1">X</font> holds <br/><font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cc0sp2.html#K6" title="CC0SP2:func.6">CC_0_Functions</a> <font color="Maroon" title="c1">X</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">u</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="cfuncdom.html#K8" title="CFUNCDOM:func.8">CAlgebra</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cc0sp2.html#K6" title="CC0SP2:func.6">CC_0_Functions</a> <font color="Maroon" title="c1">X</font> implies <font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cc0sp2.html#K6" title="CC0SP2:func.6">CC_0_Functions</a> <font color="Maroon" title="c1">X</font> )</span><br/>



<span class="kw">assume </span><a NAME="E1:63"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cc0sp2.html#K6" title="CC0SP2:func.6">CC_0_Functions</a> <font color="Maroon" title="c1">X</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cc0sp2.html#K6" title="CC0SP2:func.6">CC_0_Functions</a> <font color="Maroon" title="c1">X</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c6">u1</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a><span class="kw"> such that </span><br/><a NAME="E3:63"/><span class="lab"><font color="Green" title="E39">A2</font></span>: 
( <font color="Maroon" title="c6">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">u</font> &amp; <font color="Maroon" title="c6">u1</font> is  <a href="cc0sp2.html#V1" title="CC0SP2:attr.1">continuous</a>  &amp;  ex <font color="Olive" title="b1">Y1</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> st <br/>( <font color="Olive" title="b1">Y1</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  &amp; (  for <font color="Olive" title="b2">A1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b2">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c6">u1</font> holds <br/> <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Olive" title="b2">A1</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Olive" title="b1">Y1</font> ) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:63"><span class="lab"><font color="Green" title="E38">A1</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c7">Y1</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E5:63"/><span class="lab"><font color="Green" title="E40">A3</font></span>: 
( <font color="Maroon" title="c7">Y1</font> is  <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  &amp; (  for <font color="Olive" title="b1">A1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">A1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c6">u1</font> holds <br/> <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Olive" title="b1">A1</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">Y1</font> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E39">A2</font></span></a></span>;<br/>
<a NAME="E6:63"/><span class="lab"><font color="Green" title="E41">A4</font></span>: 
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cc0sp2.html#K2" title="CC0SP2:func.2">CContinuousFunctions</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E39">A2</font></span></a></span>;<br/>
<a NAME="E7:63"/>
<font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cc0sp2.html#K2" title="CC0SP2:func.2">CContinuousFunctions</a> <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:63"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="ref" href="cc0sp1.html#D2" title="CC0SP1:def.2">CC0SP1:def 2</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c8">fau</font> being   <a href="cc0sp2.html#V1" title="CC0SP2:attr.1">continuous</a>  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a><span class="kw"> such that </span><br/><a NAME="E9:63"/><span class="lab"><font color="Green" title="E42">A5</font></span>: 
<font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">fau</font>
 ;<br/>
<a NAME="E10:63"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E11:63"/><span class="kw">then </span><span class="lab"><font color="Green" title="E43">A6</font></span>: 
 <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c6">u1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#T37" title="PRE_POLY:th.37">PRE_POLY:37</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c9">A1</font> =  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c6">u1</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> ;<br/>
<a NAME="E13:63"/><span class="lab"><font color="Green" title="E44">A7</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E14:63"/>
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Maroon" title="c6">u1</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="c6">u1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>;<br/>
<a NAME="E15:63"/><span class="kw">then </span><span class="lab"><font color="Green" title="E45">A8</font></span>: 
 <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Maroon" title="c6">u1</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_poly.html#T37" title="PRE_POLY:th.37">PRE_POLY:37</a>, <a class="txt" href="#E13:63"><span class="lab"><font color="Green" title="E44">A7</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c10">A1</font> =  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <font color="Maroon" title="c6">u1</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:63"><span class="lab"><font color="Green" title="E43">A6</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c11">A3</font> =  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Maroon" title="c6">u1</font></span>)</span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:63"><span class="lab"><font color="Green" title="E45">A8</font></span></a></span>;<br/>
<a NAME="E18:63"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c10">A1</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">Y1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:63"><span class="lab"><font color="Green" title="E40">A3</font></span></a></span>;<br/>
<a NAME="E19:63"/><span class="kw">then </span><span class="lab"><font color="Green" title="E46">A9</font></span>: 
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c10">A1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c7">Y1</font>
 
;<br/>
<a NAME="E20:63"/>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c11">A3</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c10">A1</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pre_topc.html#T19" title="PRE_TOPC:th.19">PRE_TOPC:19</a>, <a class="ref" href="cc0sp2.html#T34" target="_self" title="CC0SP2:th.34">Th33</a></span>;<br/>
<a NAME="E21:63"/><span class="kw">then </span><span class="lab"><font color="Green" title="E47">A10</font></span>: 
 for <font color="Olive" title="b1">A3</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">A3</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_poly.html#K13" title="PRE_POLY:func.13">support</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Maroon" title="c6">u1</font></span>)</span> holds <br/> <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Olive" title="b1">A3</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c7">Y1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:63"><span class="lab"><font color="Green" title="E46">A9</font></span></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c12">uu1</font> = <font color="Maroon" title="c5">u</font> as    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>) ;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c13">fau1</font> = <font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">u</font> as    <a href="funct_2.html#M2" title="FUNCT_2:mode.2">Element</a> of  <a href="funct_2.html#K9" title="FUNCT_2:func.9">Funcs</a> ( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>) ;<br/>
<a NAME="E24:63"/><span class="lab"><font color="Green" title="E48">A11</font></span>: 
 for <font color="Olive" title="b1">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> holds  <font color="Maroon" title="c13">fau1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">uu1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="cfuncdom.html#T4" title="CFUNCDOM:th.4">CFUNCDOM:4</a></span>;<br/>
<a NAME="E25:63"/><span class="lab"><font color="Green" title="E49">A12</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c13">fau1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E26:63"/><span class="lab"><font color="Green" title="E50">A13</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c6">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></span>;<br/>
<a NAME="E27:63"/>
 for <font color="Olive" title="b1">c</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c13">fau1</font> holds <br/><font color="Maroon" title="c13">fau1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">c</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="63_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c14">c</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c14">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c13">fau1</font> implies <font color="Maroon" title="c13">fau1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">c</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:63_1"/>
<font color="Maroon" title="c14">c</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c13">fau1</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c13">fau1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">c</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">c1</font> = <font color="Maroon" title="c14">c</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> ;<br/>
<span class="kw">thus </span><font color="Maroon" title="c13">fau1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">c</font> = 
<font color="Maroon" title="c4">a</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">uu1</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c15">c1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E24:63"><span class="lab"><font color="Green" title="E48">A11</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c4">a</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">u1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c14">c</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:63"><span class="lab"><font color="Green" title="E39">A2</font></span></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/>


</div><span class="kw">end;</span></div>
<a NAME="E28:63"/><span class="kw">then </span>
<font color="Maroon" title="c13">fau1</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c4">a</font> <a href="valued_1.html#K25" title="VALUED_1:func.25">(#)</a> <font color="Maroon" title="c6">u1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:63"><span class="lab"><font color="Green" title="E49">A12</font></span></a>, <a class="txt" href="#E26:63"><span class="lab"><font color="Green" title="E50">A13</font></span></a>, <a class="ref" href="valued_1.html#D5" title="VALUED_1:def.5">VALUED_1:def 5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E29:63"/>
<font color="Maroon" title="c4">a</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="cc0sp2.html#K6" title="CC0SP2:func.6">CC_0_Functions</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:63"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="txt" href="#E5:63"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="txt" href="#E21:63"><span class="lab"><font color="Green" title="E47">A10</font></span></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/>


</div>
