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<b>let </b><font color="Maroon" title="c1">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</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">g</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">z</font> being  <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><br/> for <font color="Olive" title="b3">seq</font> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b3">seq</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a> &amp;  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Olive" title="b3">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">g</font> holds <br/>(  <a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Olive" title="b3">seq</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b1">g</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p2">(<span class="default"><font color="Olive" title="b2">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Olive" title="b3">seq</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b2">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Olive" title="b1">g</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/><b>let </b><font color="Maroon" title="c2">g</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font>; <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="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a><br/> for <font color="Olive" title="b2">seq</font> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b2">seq</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a> &amp;  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Olive" title="b2">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> holds <br/>(  <a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Olive" title="b2">seq</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">g</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p2">(<span class="default"><font color="Olive" title="b1">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Olive" title="b2">seq</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive" title="b1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/><b>let </b><font color="Maroon" title="c3">z</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</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">seq</font> being  <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>  st <font color="Olive" title="b1">seq</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a> &amp;  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Olive" title="b1">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> holds <br/>(  <a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Olive" title="b1">seq</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">g</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Olive" title="b1">seq</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/><b>let </b><font color="Maroon" title="c4">seq</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">seq</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a> &amp;  <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c4">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font> implies (  <a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c4">seq</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">g</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c4">seq</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  ) )</span><br/>







<b>assume </b><b>that </b><br/><a NAME="E1:43"/><i><font color="Green" title="E28">A1</font></i>: 
<font color="Maroon" title="c4">seq</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>
 <b>and </b><br/><a NAME="E2:43"/><i><font color="Green" title="E29">A2</font></i>: 
 <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <font color="Maroon" title="c4">seq</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">g</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c4">seq</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">g</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c4">seq</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )</span><br/>

<a NAME="E3:43"/><i><font color="Green" title="E30">A3</font></i>: 
<font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c4">seq</font> is <a href="clvect_2.html#V1" title="CLVECT_2:attr.1">convergent</a>
 
<b>by </b><i><a class="txt" href="clvect_2.html#E1:43"><i><font color="Green" title="E28">A1</font></i></a>, <a class="ref" href="clvect_2.html#T5" target="_self" title="CLVECT_2:th.5">Th5</a></i>;<br/>
<a NAME="E4:43"/>
 <a href="clvect_2.html#K1" title="CLVECT_2:func.1">lim</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c4">seq</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">g</font>
 
<b>by </b><i><a class="txt" href="clvect_2.html#E1:43"><i><font color="Green" title="E28">A1</font></i></a>, <a class="txt" href="clvect_2.html#E2:43"><i><font color="Green" title="E29">A2</font></i></a>, <a class="ref" href="clvect_2.html#T15" target="_self" title="CLVECT_2:th.15">Th15</a></i>;<br/>
<b>hence </b><a NAME="E5:43"/>
(  <a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c4">seq</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">g</font></span>)</span> is <a href="seq_2.html#V4" title="SEQ_2:attr.4">convergent</a> &amp;  <a href="seq_2.html#K2" title="SEQ_2:func.2">lim</a> <span class="p1">(<span class="default"><a href="clvect_2.html#K3" title="CLVECT_2:func.3">dist</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K7" title="CLVECT_1:func.7">*</a> <font color="Maroon" title="c4">seq</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c3">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">g</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  )
 <b>by </b><i><a class="txt" href="clvect_2.html#E3:43"><i><font color="Green" title="E30">A3</font></i></a>, <a class="ref" href="clvect_2.html#T24" target="_self" title="CLVECT_2:th.24">Th24</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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