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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">x</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">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#V2" title="CLVECT_2:attr.2">Cauchy</a> holds <br/><font color="Olive" title="b2">seq</font> <a href="normsp_1.html#K5" title="NORMSP_1:func.5">-</a> <font color="Olive" title="b1">x</font> is <a href="clvect_2.html#V2" title="CLVECT_2:attr.2">Cauchy</a></span><br/><b>let </b><font color="Maroon" title="c2">x</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">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#V2" title="CLVECT_2:attr.2">Cauchy</a> holds <br/><font color="Olive" title="b1">seq</font> <a href="normsp_1.html#K5" title="NORMSP_1:func.5">-</a> <font color="Maroon" title="c2">x</font> is <a href="clvect_2.html#V2" title="CLVECT_2:attr.2">Cauchy</a></span><br/><b>let </b><font color="Maroon" title="c3">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="c3">seq</font> is <a href="clvect_2.html#V2" title="CLVECT_2:attr.2">Cauchy</a> implies <font color="Maroon" title="c3">seq</font> <a href="normsp_1.html#K5" title="NORMSP_1:func.5">-</a> <font color="Maroon" title="c2">x</font> is <a href="clvect_2.html#V2" title="CLVECT_2:attr.2">Cauchy</a> )</span><br/>





<b>assume </b><a NAME="E1:71"/>
<font color="Maroon" title="c3">seq</font> is <a href="clvect_2.html#V2" title="CLVECT_2:attr.2">Cauchy</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">seq</font> <a href="normsp_1.html#K5" title="NORMSP_1:func.5">-</a> <font color="Maroon" title="c2">x</font> is <a href="clvect_2.html#V2" title="CLVECT_2:attr.2">Cauchy</a></span><br/>

<a NAME="E2:71"/><b>then </b>
<font color="Maroon" title="c3">seq</font> <a href="bhsp_1.html#K7" title="BHSP_1:func.7">+</a> <span class="p1">(<span class="default"><a href="algstr_0.html#K4" title="ALGSTR_0:func.4">-</a> <font color="Maroon" title="c2">x</font></span>)</span> is <a href="clvect_2.html#V2" title="CLVECT_2:attr.2">Cauchy</a>
 
<b>by </b><i><a class="ref" href="clvect_2.html#T63" target="_self" title="CLVECT_2:th.63">Th63</a></i>;<br/>
<b>hence </b><a NAME="E3:71"/>
<font color="Maroon" title="c3">seq</font> <a href="normsp_1.html#K5" title="NORMSP_1:func.5">-</a> <font color="Maroon" title="c2">x</font> is <a href="clvect_2.html#V2" title="CLVECT_2:attr.2">Cauchy</a>
 <b>by </b><i><a class="ref" href="csspace.html#T78" title="CSSPACE:th.78">CSSPACE:78</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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