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<span class="kw">let </span><font color="Maroon" title="c4">X</font> be   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</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">seq1</font>, <font color="Olive" title="b2">seq2</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>  holds <br/><font color="Olive" title="b1">seq1</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">-</a> <font color="Olive" title="b2">seq2</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> 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" 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="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>  implies <font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">-</a> <font color="Maroon" title="c6">seq2</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="E1:53"/><span class="lab"><font color="Green" title="E27">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="E2:53"/><span class="lab"><font color="Green" title="E28">A2</font></span>: 
<font color="Maroon" title="c6">seq2</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</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"> <font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">-</a> <font color="Maroon" title="c6">seq2</font> is  <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a> </span><br/>

<span class="kw">set </span><font color="Maroon" title="c7">seq</font> = <font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">-</a> <font color="Maroon" title="c6">seq2</font>;<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="E4:53"/><span class="lab"><font color="Green" title="E29">A3</font></span>: 
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon" title="c5">seq1</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</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="#E1:53"><span class="lab"><font color="Green" title="E27">A1</font></span></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="E6:53"/><span class="lab"><font color="Green" title="E30">A4</font></span>: 
 for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a> holds  <font color="Maroon" title="c6">seq2</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</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="#E2:53"><span class="lab"><font color="Green" title="E28">A2</font></span></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" onmouseover="rs('valued_0/D20')" onmouseout="rh()">VALUED_0:def 20</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">b<sub>1</sub></font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a>  holds  <span class="p1">(<span class="default"><font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">-</a> <font color="Maroon" title="c6">seq2</font></span>)</span> <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="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</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"><font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">-</a> <font color="Maroon" title="c6">seq2</font></span>)</span> <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/>

<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c5">seq1</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">-</a> <font color="Maroon" title="c6">seq2</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</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#K8" title="NAT_1:func.8">.</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#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c11">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normsp_1.html#D3" onmouseover="rs('normsp_1/D3')" onmouseout="rh()">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#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c11">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:53"><span class="lab"><font color="Green" title="E29">A3</font></span></a></span>
<br/>.= 
<font color="Maroon" title="c10">z</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:53"><span class="lab"><font color="Green" title="E30">A4</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/>


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