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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be   <a href="normsp_1.html#NM1" title="NORMSP_1:NM.1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">h</font> be   <a href="struct_0.html#NM10" title="STRUCT_0:NM.10">PartFunc</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>;<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">S</font>;<br/>







<b>assume </b><a NAME="E1:30"/><i><font color="Green" title="E27">A1</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">seq</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font>
 ;<br/>

<a NAME="E2:30"/><b>then </b><i><font color="Green" title="E28">A2</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">seq</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span>
 
<b>by </b><i><a class="ref" href="nfcont_1.html#D2" target="_self" title="NFCONT_1:def.2">Def2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="30_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c5">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ;<br/><a NAME="E1:30_1"/>
<font color="Maroon" title="c4">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">seq</font>
 <b>by </b><i><a class="ref" href="nfcont_1.html#T6" target="_self" title="NFCONT_1:th.6">Th6</a></i>;<br/><a NAME="E2:30_1"/><b>then </b>
<font color="Maroon" title="c4">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font>
 <b>by </b><i><a class="txt" href="nfcont_1.html#E1:30"><i><font color="Green" title="E27">A1</font></i></a></i>;<br/><a NAME="E3:30_1"/><b>then </b><i><font color="Green" title="E29">A3</font></i>: 
<font color="Maroon" title="c4">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span>
 <b>by </b><i><a class="ref" href="nfcont_1.html#D2" target="_self" title="NFCONT_1:def.2">Def2</a></i>;<br/><b>thus </b><span class="p1"><a href="normsp_1.html#K7" title="NORMSP_1:func.7">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c4">seq</font></span>)</span></span><a href="normsp_1.html#K7" title="NORMSP_1:func.7">.||</a></span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">n</font> = 
<span class="p1"><a href="normsp_1.html#K1" title="NORMSP_1:func.1">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c4">seq</font></span>)</span> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span><a href="normsp_1.html#K1" title="NORMSP_1:func.1">.||</a></span>
<b>by </b><i><a class="ref" href="normsp_1.html#D10" title="NORMSP_1:def.10">NORMSP_1:def 10</a></i>
<br/>.= 
<span class="p1"><a href="normsp_1.html#K1" title="NORMSP_1:func.1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font></span>)</span></span>)</span></span><a href="normsp_1.html#K1" title="NORMSP_1:func.1">.||</a></span>
<b>by </b><i><a class="txt" href="nfcont_1.html#E1:30"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="nfcont_1.html#T8" target="_self" title="NFCONT_1:th.8">Th8</a></i>
<br/>.= 
<span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="seq_1.html#K1" title="SEQ_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font></span>)</span>
<b>by </b><i><a class="txt" href="nfcont_1.html#E3:30_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="nfcont_1.html#D2" target="_self" title="NFCONT_1:def.2">Def2</a></i>
<br/>.= 
<span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">seq</font> <a href="normsp_1.html#K2" title="NORMSP_1:func.2">.</a> <font color="Maroon" title="c5">n</font></span>)</span>
<b>by </b><i><a class="txt" href="nfcont_1.html#E3:30_1"><i><font color="Green" title="E29">A3</font></i></a>, <a class="ref" href="partfun1.html#D8" title="PARTFUN1:def.8">PARTFUN1:def 8</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="nfcont_1.html#K3" title="NFCONT_1:func.3">*</a> <font color="Maroon" title="c4">seq</font></span>)</span> <a href="seq_1.html#K2" title="SEQ_1:func.2">.</a> <font color="Maroon" title="c5">n</font>
<b>by </b><i><a class="txt" href="nfcont_1.html#E2:30"><i><font color="Green" title="E28">A2</font></i></a>, <a class="ref" href="nfcont_1.html#T9" target="_self" title="NFCONT_1:th.9">Th9</a></i>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E4:30"/>
<span class="p1"><a href="normsp_1.html#K7" title="NORMSP_1:func.7">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c4">seq</font></span>)</span></span><a href="normsp_1.html#K7" title="NORMSP_1:func.7">.||</a></span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1"><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">||.</a><span class="default"><font color="Maroon" title="c3">h</font></span><a href="nfcont_1.html#K1" title="NFCONT_1:func.1">.||</a></span> <a href="nfcont_1.html#K3" title="NFCONT_1:func.3">*</a> <font color="Maroon" title="c4">seq</font>
 <b>by </b><i><a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></i>;<br/>

<b>thus </b> <a href="bhsp_1.html#K6" title="BHSP_1:func.6">-</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c4">seq</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="normsp_1.html#K6" title="NORMSP_1:func.6">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">h</font> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c4">seq</font></span>)</span>
<b>by </b><i><a class="ref" href="nfcont_1.html#T2" target="_self" title="NFCONT_1:th.2">Th2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="real_1.html#K1" title="REAL_1:func.1">-</a> 1</span>)</span> <a href="vfunct_1.html#K4" title="VFUNCT_1:func.4">(#)</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c4">seq</font>
<b>by </b><i><a class="txt" href="nfcont_1.html#E1:30"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="nfcont_1.html#T20" target="_self" title="NFCONT_1:th.20">Th20</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="vfunct_1.html#K6" title="VFUNCT_1:func.6">-</a> <font color="Maroon" title="c3">h</font></span>)</span> <a href="nfcont_1.html#K2" title="NFCONT_1:func.2">*</a> <font color="Maroon" title="c4">seq</font>
<b>by </b><i><a class="ref" href="vfunct_1.html#T29" title="VFUNCT_1:th.29">VFUNCT_1:29</a></i>
;<br/>


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