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<span class="kw">let </span><font color="Maroon" title="c4">X</font> be   <a href="csspace.html#NM1" title="CSSPACE:NM.1">ComplexUnitarySpace</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">seq1</font>, <font color="Olive" title="b2">seq2</font>, <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="c4">X</font>  st <font color="Olive" title="b1">seq1</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  &amp; <font color="Olive" title="b2">seq2</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  &amp; <font color="Olive" title="b3">seq</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Olive" title="b1">seq1</font> <a href="normsp_1.html#K3" title="NORMSP_1:func.3">-</a> <font color="Olive" title="b2">seq2</font> holds <br/><font color="Olive" title="b3">seq</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">seq1</font>, <font color="Maroon" title="c6">seq2</font>, <font color="Maroon" title="c7">seq</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c4">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="c5">seq1</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  &amp; <font color="Maroon" title="c6">seq2</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  &amp; <font color="Maroon" title="c7">seq</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K3" title="NORMSP_1:func.3">-</a> <font color="Maroon" title="c6">seq2</font> implies <font color="Maroon" title="c7">seq</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:84"/><span class="lab"><font color="Green" title="E59">A1</font></span>: 
<font color="Maroon" title="c5">seq1</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> 
 <span class="kw">and </span><br/><a NAME="E2:84"/><span class="lab"><font color="Green" title="E60">A2</font></span>: 
<font color="Maroon" title="c6">seq2</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> 
 <span class="kw">and </span><br/><a NAME="E3:84"/><span class="lab"><font color="Green" title="E61">A3</font></span>: 
<font color="Maroon" title="c7">seq</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K3" title="NORMSP_1:func.3">-</a> <font color="Maroon" title="c6">seq2</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="c7">seq</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c8">x</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">X</font><span class="kw"> such that </span><br/><a NAME="E5:84"/><span class="lab"><font color="Green" title="E62">A4</font></span>: 
 for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c5">seq1</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:84"><span class="lab"><font color="Green" title="E59">A1</font></span></a>, <a class="ref" href="valued_0.html#D18" title="VALUED_0:def.18">VALUED_0:def 18</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c9">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">X</font><span class="kw"> such that </span><br/><a NAME="E7:84"/><span class="lab"><font color="Green" title="E63">A5</font></span>: 
 for <font color="Olive" title="b1">n</font> being   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a> holds  <font color="Maroon" title="c6">seq2</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Olive" title="b1">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:84"><span class="lab"><font color="Green" title="E60">A2</font></span></a>, <a class="ref" href="valued_0.html#D18" title="VALUED_0:def.18">VALUED_0:def 18</a></span>;<br/>
<span class="kw">take </span><font color="Maroon" title="c10">z</font> = <font color="Maroon" title="c8">x</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <font color="Maroon" title="c9">y</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="valued_0.html#D20" title="VALUED_0:def.20">VALUED_0:def 20</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">b<sub>1</sub></font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds  <font color="Maroon" title="c7">seq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">z</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c11">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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="c7">seq</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c11">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">z</font></span><br/>

<a NAME="E8:84"/>
<font color="Maroon" title="c11">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ordinal1.html#D12" title="ORDINAL1:def.12">ORDINAL1:def 12</a></span>;<br/>
<span class="kw">hence </span><font color="Maroon" title="c7">seq</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c11">n</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">seq1</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c11">n</font></span>)</span> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">seq2</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c11">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:84"><span class="lab"><font color="Green" title="E61">A3</font></span></a>, <a class="ref" href="normsp_1.html#D3" title="NORMSP_1:def.3">NORMSP_1:def 3</a></span>
<br/>.= 
<font color="Maroon" title="c8">x</font> <a href="algstr_0.html#K5" title="ALGSTR_0:func.5">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">seq2</font> <a href="nat_1.html#K6" title="NAT_1:func.6">.</a> <font color="Maroon" title="c11">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:84"><span class="lab"><font color="Green" title="E62">A4</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c10">z</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:84"><span class="lab"><font color="Green" title="E63">A5</font></span></a></span>
;<br/> <a class="txt" 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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