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<b>let </b><font color="Maroon">S</font> be  non <a href="realset2.html#V3">trivial</a> <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">T</font> be  non <a href="realset2.html#V3">trivial</a> <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">U</font> be  non <a href="realset2.html#V3">trivial</a> <a href="normsp_1.html#NM1">RealNormSpace</a>;<br/><b>let </b><font color="Maroon">R</font> be   <a href="ndiff_1.html#NM1">REST</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">L</font> be  <a href="lopban_1.html#V3">bounded</a> <a href="lopban_1.html#NM1">LinearOperator</a> of <font color="Maroon">T</font>,<font color="Maroon">U</font>;<br/>









<b>consider </b><font color="Maroon">K</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E2:13"/><i><font color="Green">E34</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">K</font>
 <b>and </b><br/><a NAME="E3:13"/><i><font color="Green">E39</font></i>: 
for <font color="Olive">z</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font> holds  <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="funct_2.html#K3">.</a> <font color="Olive">z</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">K</font> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Olive">z</font></span><a href="normsp_1.html#K1">.||</a></span>
 <b>by </b><i><a class="ref" href="lopban_1.html#D9">LOPBAN_1:def 9</a></i>;<br/>
<a NAME="E4:13"/><i><font color="Green">E40</font></i>: 
0 <a href="real_1.html#K3">+</a> <font color="Maroon">K</font> <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="real_1.html#K3">+</a> <font color="Maroon">K</font>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/>
<a NAME="E5:13"/><b>then </b><i><font color="Green">E42</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="real_1.html#K3">+</a> <font color="Maroon">K</font>
 
<b>by </b><i/>;<br/>
<a NAME="E6:13"/><i><font color="Green">E43</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">L</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E7:13"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">R</font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i><a class="ref" href="ndiff_1.html#D5">NDIFF_1:def 5</a></i>;<br/>
<a NAME="E8:13"/><b>then </b><i><font color="Green">E45</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">R</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>
<a NAME="E9:13"/><i><font color="Green">E46</font></i>: 
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">R</font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<b>then </b> <a href="relset_1.html#K4">dom</a> <span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">R</font></span>)</span> = 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">R</font>
<b>by </b><i><a class="ref" href="relat_1.html#T46">RELAT_1:46</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
<b>by </b><i>, <a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>
;<br/>
<a NAME="E11:13"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">L</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">R</font> is <a href="partfun1.html#V1">total</a>
 
<b>by </b><i><a class="ref" href="partfun1.html#D4">PARTFUN1:def 4</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">ee</font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>assume </b><a NAME="E1:13_2"/><i><font color="Green">E48</font></i>: 
<font color="Maroon">ee</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><b>set </b><font color="Maroon">e</font> = <font color="Maroon">ee</font> <a href="real_1.html#K6">/</a> 2;<br/><a NAME="E2:13_2"/><i><font color="Green">E51</font></i>: 
<font color="Maroon">ee</font> <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i>, <a class="ref" href="seq_2.html#T3">SEQ_2:3</a></i>;<br/><a NAME="E3:13_2"/><i><font color="Green">E52</font></i>: 
<font color="Maroon">ee</font> <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">ee</font>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T218">XREAL_1:218</a></i>;<br/><b>set </b><font color="Maroon">e1</font> = <span class="p1">(<span class="default"><font color="Maroon">ee</font> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <font color="Maroon">K</font></span>)</span>;<br/><a NAME="E4:13_2"/><i><font color="Green">E53</font></i>: 
0 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <font color="Maroon">K</font></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">ee</font> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <font color="Maroon">K</font></span>)</span>
 <b>by </b><i>, , , <a class="ref" href="real_1.html#T73">REAL_1:73</a></i>;<br/><a NAME="E5:13_2"/>
<font color="Maroon">R</font> is <a href="partfun1.html#V1">total</a>
 <b>by </b><i><a class="ref" href="ndiff_1.html#D5">NDIFF_1:def 5</a></i>;<br/><b>then consider </b><font color="Maroon">d</font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E7:13_2"/><i><font color="Green">E54</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">d</font>
 <b>and </b><br/><a NAME="E8:13_2"/><i><font color="Green">E55</font></i>: 
for <font color="Olive">h</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>  st <font color="Olive">h</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">S</font> &amp; <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Olive">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">d</font> holds <br/><span class="p1">(<span class="default"><span class="p2"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Olive">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Olive">h</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">ee</font> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <font color="Maroon">K</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="ndiff_1.html#T26">NDIFF_1:26</a></i>;<br/><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="13_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">h</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>;<br/><b>assume </b><b>that </b><br/><a NAME="E1:13_2_1"/><i><font color="Green">E56</font></i>: 
<font color="Maroon">h</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">S</font>
 <b>and </b><br/><a NAME="E2:13_2_1"/><i><font color="Green">E57</font></i>: 
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">d</font>
 ;<br/><i><font color="Green">E58</font></i>: <font color="Maroon">L</font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span> = 
<font color="Maroon">L</font> <a href="finseq_4.html#K4">/.</a> <span class="p1">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span>
<b>by </b><i>, <a class="ref" href="finseq_4.html#D4">FINSEQ_4:def 4</a></i>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon">L</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">R</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font>
<b>by </b><i>, , <a class="ref" href="partfun2.html#T10">PARTFUN2:10</a></i>
;<br/><a NAME="E4:13_2_1"/>
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i>, <a class="ref" href="normsp_1.html#D2">NORMSP_1:def 2</a></i>;<br/><a NAME="E5:13_2_1"/><b>then </b>
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="normsp_1.html#T8">NORMSP_1:8</a></i>;<br/><a NAME="E6:13_2_1"/><b>then </b><i><font color="Green">E59</font></i>: 
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K2">"</a>  <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>by </b><i><a class="ref" href="xreal_1.html#T124">XREAL_1:124</a></i>;<br/><a NAME="E7:13_2_1"/><i><font color="Green">E60</font></i>: 
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">K</font> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span>
 <b>by </b><i/>;<br/><a NAME="E8:13_2_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span>
 <b>by </b><i><a class="ref" href="normsp_1.html#T8">NORMSP_1:8</a></i>;<br/><a NAME="E9:13_2_1"/><b>then </b>
<font color="Maroon">K</font> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="real_1.html#K3">+</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E10:13_2_1"/><b>then </b>
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="real_1.html#K3">+</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><a NAME="E11:13_2_1"/><b>then </b><i><font color="Green">E62</font></i>: 
<span class="p1">(<span class="default"><span class="p2"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">K</font> <a href="real_1.html#K3">+</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E12:13_2_1"/>
<span class="p1">(<span class="default"><span class="p2"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">ee</font> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K3">+</a> <font color="Maroon">K</font></span>)</span>
 <b>by </b><i>, , </i>;<br/><a NAME="E13:13_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="real_1.html#K3">+</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="real_1.html#K3">+</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">ee</font> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K3">+</a> <font color="Maroon">K</font></span>)</span></span>)</span>
 <b>by </b><i>, <a class="ref" href="xreal_1.html#T66">XREAL_1:66</a></i>;<br/><a NAME="E14:13_2_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon">K</font> <a href="real_1.html#K3">+</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p2"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">ee</font> <a href="real_1.html#K6">/</a> 2
 <b>by </b><i>, , <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/><a NAME="E15:13_2_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">L</font> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default"><font color="Maroon">R</font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">ee</font> <a href="real_1.html#K6">/</a> 2
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/><b>hence </b><a NAME="E16:13_2_1"/>
<span class="p1">(<span class="default"><span class="p2"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">R</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">h</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">ee</font>
 <b>by </b><i>, , <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/></div><b>end;</b></div><b>hence </b><a NAME="E10:13_2"/>
 ex <font color="Olive">d</font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">d</font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; ( for <font color="Olive">h</font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>  st <font color="Olive">h</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="rlvect_1.html#K1">0.</a> <font color="Maroon">S</font> &amp; <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Olive">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">d</font> holds <br/><span class="p1">(<span class="default"><span class="p2"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Olive">h</font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K2">"</a> </span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">L</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">R</font></span>)</span> <a href="finseq_4.html#K4">/.</a> <font color="Olive">h</font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">ee</font> ) )
 <b>by </b><i/>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E13:13"/>
<font color="Maroon">L</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">R</font> is   <a href="ndiff_1.html#NM1">REST</a> of <font color="Maroon">S</font>,<font color="Maroon">U</font>
 <b>by </b><i>, <a class="ref" href="ndiff_1.html#T26">NDIFF_1:26</a></i>;<br/>


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