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<span class="kw">let </span><font color="Maroon" title="c4">a</font> be   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</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">X</font> being   <a href="bhsp_1.html#NM1" title="BHSP_1:NM.1">RealUnitarySpace</a><br/>  for <font color="Olive" title="b2">seq1</font>, <font color="Olive" title="b3">seq2</font> being   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Olive" title="b1">X</font> holds  <font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">seq1</font> <a href="bhsp_1.html#K6" title="BHSP_1:func.6">+</a> <font color="Olive" title="b3">seq2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Olive" title="b2">seq1</font></span>)</span> <a href="bhsp_1.html#K6" title="BHSP_1:func.6">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Olive" title="b3">seq2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c5">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="c5">X</font> holds  <font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">seq1</font> <a href="bhsp_1.html#K6" title="BHSP_1:func.6">+</a> <font color="Olive" title="b2">seq2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Olive" title="b1">seq1</font></span>)</span> <a href="bhsp_1.html#K6" title="BHSP_1:func.6">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Olive" title="b2">seq2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c6">seq1</font>, <font color="Maroon" title="c7">seq2</font> be   <a href="struct_0.html#NM9" title="STRUCT_0:NM.9">sequence</a> of <font color="Maroon" title="c5">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="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c6">seq1</font> <a href="bhsp_1.html#K6" title="BHSP_1:func.6">+</a> <font color="Maroon" title="c7">seq2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Maroon" title="c6">seq1</font></span>)</span> <a href="bhsp_1.html#K6" title="BHSP_1:func.6">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Maroon" title="c7">seq2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="funct_2.html#D8" onmouseover="rs('funct_2/D8')" onmouseout="rh()">FUNCT_2:def 8</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="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">seq1</font> <a href="bhsp_1.html#K6" title="BHSP_1:func.6">+</a> <font color="Maroon" title="c7">seq2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Maroon" title="c6">seq1</font></span>)</span> <a href="bhsp_1.html#K6" title="BHSP_1:func.6">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Maroon" title="c7">seq2</font></span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">n</font></span><br/>









<span class="kw">thus </span><span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">seq1</font> <a href="bhsp_1.html#K6" title="BHSP_1:func.6">+</a> <font color="Maroon" title="c7">seq2</font></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font> = 
<font color="Maroon" title="c4">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">seq1</font> <a href="bhsp_1.html#K6" title="BHSP_1:func.6">+</a> <font color="Maroon" title="c7">seq2</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normsp_1.html#D5" onmouseover="rs('normsp_1/D5')" onmouseout="rh()">NORMSP_1:def 5</a></span>
<br/>.= 
<font color="Maroon" title="c4">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">seq1</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">seq2</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normsp_1.html#D2" onmouseover="rs('normsp_1/D2')" onmouseout="rh()">NORMSP_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">seq1</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">seq2</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D5" onmouseover="rs('rlvect_1/D5')" onmouseout="rh()">RLVECT_1:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Maroon" title="c6">seq1</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="rlvect_1.html#K1" title="RLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c7">seq2</font> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normsp_1.html#D5" onmouseover="rs('normsp_1/D5')" onmouseout="rh()">NORMSP_1:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Maroon" title="c6">seq1</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Maroon" title="c7">seq2</font></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normsp_1.html#D5" onmouseover="rs('normsp_1/D5')" onmouseout="rh()">NORMSP_1:def 5</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Maroon" title="c6">seq1</font></span>)</span> <a href="bhsp_1.html#K6" title="BHSP_1:func.6">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">a</font> <a href="normsp_1.html#K4" title="NORMSP_1:func.4">*</a> <font color="Maroon" title="c7">seq2</font></span>)</span></span>)</span> <a href="nat_1.html#K8" title="NAT_1:func.8">.</a> <font color="Maroon" title="c8">n</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="normsp_1.html#D2" onmouseover="rs('normsp_1/D2')" onmouseout="rh()">NORMSP_1:def 2</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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