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<b>let </b><font color="Maroon">c<sub>6</sub></font>, <font color="Maroon">c<sub>7</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:8_1_2"/><i><font color="Green">E6</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="nfcont_1.html#M1">Neighbourhood</a> of <font color="Maroon">c<sub>4</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/>ex <font color="Olive">b<sub>3</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; ( for <font color="Olive">b<sub>4</sub></font> being  <a href="real_1.html#NM1">Real</a> st  <a href="complex1.html#K18">abs</a> <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> holds <br/><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"><span class="p4">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>2</sub></font> ) ) ) )
 <b>and </b><br/><a NAME="E2:8_1_2"/><i><font color="Green">E7</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being   <a href="nfcont_1.html#M1">Neighbourhood</a> of <font color="Maroon">c<sub>4</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font> &amp; ( for <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/>ex <font color="Olive">b<sub>3</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; ( for <font color="Olive">b<sub>4</sub></font> being  <a href="real_1.html#NM1">Real</a> st  <a href="complex1.html#K18">abs</a> <font color="Olive">b<sub>4</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Olive">b<sub>1</sub></font> holds <br/><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"><span class="p4">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>2</sub></font> ) ) ) )
 ;<br/>

<b>consider </b><font color="Maroon">c<sub>8</sub></font> being    <a href="nfcont_1.html#M1">Neighbourhood</a> of <font color="Maroon">c<sub>4</sub></font><b> such that </b><br/><a NAME="E4:8_1_2"/>
<font color="Maroon">c<sub>8</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E5:8_1_2"/><i><font color="Green">E8</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/>ex <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="real_1.html#NM1">Real</a> st  <a href="complex1.html#K18">abs</a> <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font> holds <br/><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"><span class="p4">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="ndiff_2.html#E1:8_1_2"><i><font color="Green">E6</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>9</sub></font> being    <a href="nfcont_1.html#M1">Neighbourhood</a> of <font color="Maroon">c<sub>4</sub></font><b> such that </b><br/><a NAME="E7:8_1_2"/>
<font color="Maroon">c<sub>9</sub></font> <a href="tarski.html#R1">c=</a>  <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
 <b>and </b><br/><a NAME="E8:8_1_2"/><i><font color="Green">E9</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 holds <br/>ex <font color="Olive">b<sub>2</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0 &amp; ( for <font color="Olive">b<sub>3</sub></font> being  <a href="real_1.html#NM1">Real</a> st  <a href="complex1.html#K18">abs</a> <font color="Olive">b<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>3</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> holds <br/><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"><span class="p4">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Olive">b<sub>3</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Olive">b<sub>1</sub></font> ) )
 <b>by </b><i><a class="txt" href="ndiff_2.html#E2:8_1_2"><i><font color="Green">E7</font></i></a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>10</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/><b>assume </b><a NAME="E1:8_1_2_1"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>10</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 ;<br/><a NAME="E2:8_1_2_1"/><i><font color="Green">E11</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K6">/</a> 2
 <b>by </b><i><a class="txt" href="ndiff_2.html#E1:8_1_2_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="seq_2.html#T3">SEQ_2:3</a></i>;<br/><b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E4:8_1_2_1"/><i><font color="Green">E12</font></i>: 
<font color="Maroon">c<sub>11</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>and </b><br/><a NAME="E5:8_1_2_1"/><i><font color="Green">E13</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st  <a href="complex1.html#K18">abs</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font> holds <br/><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"><span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K6">/</a> 2
 <b>by </b><i><a class="txt" href="ndiff_2.html#E5:8_1_2"><i><font color="Green">E8</font></i></a>, <a class="txt" href="ndiff_2.html#E2:8_1_2_1"><i><font color="Green">E11</font></i></a></i>;<br/><b>consider </b><font color="Maroon">c<sub>12</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E7:8_1_2_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#NR4" target="_self">&gt;</a> 0
 <b>and </b><br/><a NAME="E8:8_1_2_1"/><i><font color="Green">E15</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st  <a href="complex1.html#K18">abs</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> holds <br/><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"><span class="p4">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K6">/</a> 2
 <b>by </b><i><a class="txt" href="ndiff_2.html#E8:8_1_2"><i><font color="Green">E9</font></i></a>, <a class="txt" href="ndiff_2.html#E2:8_1_2_1"><i><font color="Green">E11</font></i></a></i>;<br/><a NAME="E9:8_1_2_1"/><i><font color="Green">E16</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="real_1.html#NM1">Real</a> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp;  <a href="complex1.html#K18">abs</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="complex1.html#K18">abs</a> <font color="Olive">b<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>12</sub></font> &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font> &amp; <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="8_1_2_1_1"><b>proof </b></a><div class="add">

<b>consider </b><font color="Maroon">c<sub>13</sub></font> being    <a href="nfcont_1.html#M1">Neighbourhood</a> of <font color="Maroon">c<sub>4</sub></font><b> such that </b><br/><a NAME="E2:8_1_2_1_1"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>13</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>8</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="ref" href="ndiff_1.html#T1">NDIFF_1:1</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>14</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E4:8_1_2_1_1"/><i><font color="Green">E18</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>14</sub></font> &amp; <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> : <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>14</sub></font> </span>}</span>  <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>13</sub></font> )
 <b>by </b><i><a class="ref" href="nfcont_1.html#D3">NFCONT_1:def 3</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>15</sub></font> =  <a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>;<br/>
<a NAME="E5:8_1_2_1_1"/><i><font color="Green">E19</font></i>: 
(  <a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>12</sub></font> )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T17">XXREAL_0:17</a></i>;<br/>
<a NAME="E6:8_1_2_1_1"/>
0 <a href="xxreal_0.html#R1">&lt;</a>  <a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font>
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E4:8_1_2_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="ndiff_2.html#E7:8_1_2_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="xxreal_0.html#T15">XXREAL_0:15</a></i>;<br/>
<a NAME="E7:8_1_2_1_1"/><b>then </b><i><font color="Green">E20</font></i>: 
( 0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2 &amp; <span class="p1">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#R1">&lt;</a>  <a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font> )
 
<b>by </b><i><a class="ref" href="seq_2.html#T3">SEQ_2:3</a>, <a class="ref" href="xreal_1.html#T218">XREAL_1:218</a></i>;<br/>
<a NAME="E8:8_1_2_1_1"/><b>then </b><i><font color="Green">E21</font></i>: 
( <span class="p1">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>11</sub></font> &amp; <span class="p1">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>12</sub></font> )
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E5:8_1_2_1_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>16</sub></font> being   <a href="nat_1.html#NM1">Nat</a><b> such that </b><br/><a NAME="E10:8_1_2_1_1"/><i><font color="Green">E22</font></i>: 
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>16</sub></font>
 <b>by </b><i><a class="ref" href="seq_4.html#T10">SEQ_4:10</a></i>;<br/>
<a NAME="E11:8_1_2_1_1"/>
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font>
 
<b>by </b><i><a class="ref" href="nat_1.html#T18">NAT_1:18</a></i>;<br/>
<a NAME="E12:8_1_2_1_1"/><b>then </b><i><font color="Green">E23</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T38">NAT_1:38</a></i>;<br/>
<a NAME="E13:8_1_2_1_1"/>
<font color="Maroon">c<sub>16</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="ref" href="nat_1.html#T29">NAT_1:29</a></i>;<br/>
<a NAME="E14:8_1_2_1_1"/><b>then </b>
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E10:8_1_2_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E15:8_1_2_1_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">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K6">/</a> <font color="Maroon">c<sub>14</sub></font></span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>14</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E4:8_1_2_1_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="xreal_1.html#T70">XREAL_1:70</a></i>;<br/>
<a NAME="E16:8_1_2_1_1"/><b>then </b>
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></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">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="real_1.html#K4">*</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E4:8_1_2_1_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="xcmplx_1.html#T88">XCMPLX_1:88</a></i>;<br/>
<a NAME="E17:8_1_2_1_1"/><b>then </b><i><font color="Green">E24</font></i>: 
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E12:8_1_2_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="real_2.html#T178">REAL_2:178</a></i>;<br/>
<b>set </b><font color="Maroon">c<sub>17</sub></font> = <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1;<br/>
<b>set </b><font color="Maroon">c<sub>18</sub></font> =  <a href="square_1.html#K1">min</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span>;<br/>
<b>take </b>
 <a href="square_1.html#K1">min</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span>
;<br/>

<a NAME="E18:8_1_2_1_1"/>
0 <a href="nat_1.html#K1">+</a> 0 <a href="xxreal_0.html#R1">&lt;</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E12:8_1_2_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="xreal_1.html#T10">XREAL_1:10</a></i>;<br/>
<a NAME="E19:8_1_2_1_1"/><b>then </b>
0 <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="real_1.html#K4">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K2">"</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="xreal_1.html#T124">XREAL_1:124</a></i>;<br/>
<a NAME="E20:8_1_2_1_1"/><b>then </b><i><font color="Green">E25</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a> 1 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_0.html#D9">XCMPLX_0:def 9</a></i>;<br/>
<b>hence </b><a NAME="E21:8_1_2_1_1"/>
 <a href="square_1.html#K1">min</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0
 <b>by </b><i><a class="txt" href="ndiff_2.html#E7:8_1_2_1_1"><i><font color="Green">E20</font></i></a>, <a class="ref" href="xxreal_0.html#T15">XXREAL_0:15</a></i>;<br/>

<a NAME="E22:8_1_2_1_1"/><i><font color="Green">E26</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;</a>  <a href="square_1.html#K1">min</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span>
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E7:8_1_2_1_1"><i><font color="Green">E20</font></i></a>, <a class="txt" href="ndiff_2.html#E20:8_1_2_1_1"><i><font color="Green">E25</font></i></a>, <a class="ref" href="xxreal_0.html#T15">XXREAL_0:15</a></i>;<br/>
<a NAME="E23:8_1_2_1_1"/>
(  <a href="square_1.html#K1">min</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> &amp;  <a href="square_1.html#K1">min</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2 )
 
<b>by </b><i><a class="ref" href="xxreal_0.html#T17">XXREAL_0:17</a></i>;<br/>
<a NAME="E24:8_1_2_1_1"/><b>then </b>
(  <a href="square_1.html#K1">min</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="square_1.html#K1">min</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>12</sub></font> )
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E8:8_1_2_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<b>hence </b><a NAME="E25:8_1_2_1_1"/>
(  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="complex1.html#K18">abs</a> <span class="p1">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>12</sub></font> )
 <b>by </b><i><a class="txt" href="ndiff_2.html#E22:8_1_2_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>;<br/>

<a NAME="E26:8_1_2_1_1"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span> &amp; <font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1 <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="nat_1.html#K1">+</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 
<b>by </b><i><a class="ref" href="nat_1.html#T37">NAT_1:37</a>, <a class="ref" href="normsp_1.html#T8">NORMSP_1:8</a></i>;<br/>
<a NAME="E27:8_1_2_1_1"/><b>then </b><i><font color="Green">E27</font></i>: 
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span>
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E12:8_1_2_1_1"><i><font color="Green">E23</font></i></a>, <a class="ref" href="real_2.html#T201">REAL_2:201</a></i>;<br/>
<i><font color="Green">E28</font></i>: <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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> = 
<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"><span class="p4">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span><a href="normsp_1.html#K1">.||</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#D6">RLVECT_1:def 6</a></i>
<br/>.= 
<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"><span class="p4">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p5">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p5">(<span class="default"><span class="p0">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <span class="p3">(<span class="default"><a href="rlvect_1.html#K1">0.</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span>)</span></span><a href="normsp_1.html#K1">.||</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T28">RLVECT_1:28</a></i>
<br/>.= 
<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"><a href="square_1.html#K1">min</a> <span class="p4">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p5">(<span class="default"><span class="p0">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span>
<b>by </b><i><a class="ref" href="rlvect_1.html#T10">RLVECT_1:10</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="complex1.html#K18">abs</a> <span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span>
<b>by </b><i><a class="ref" href="normsp_1.html#D2">NORMSP_1:def 2</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span>
<b>by </b><i><a class="txt" href="ndiff_2.html#E22:8_1_2_1_1"><i><font color="Green">E26</font></i></a>, <a class="ref" href="absvalue.html#D1">ABSVALUE:def 1</a></i>
;<br/>
<a NAME="E29:8_1_2_1_1"/>
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span> <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="xcmplx_1.html#T100">XCMPLX_1:100</a></i>;<br/>
<a NAME="E30:8_1_2_1_1"/><b>then </b><i><font color="Green">E29</font></i>: 
<span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default">1 <a href="nat_1.html#K1">+</a> <span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E17:8_1_2_1_1"><i><font color="Green">E24</font></i></a>, <a class="txt" href="ndiff_2.html#E27:8_1_2_1_1"><i><font color="Green">E27</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E31:8_1_2_1_1"/>
( 0 <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span> &amp;  <a href="square_1.html#K1">min</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="xxreal_0.html#R1">&lt;=</a> 1 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span> )
 
<b>by </b><i><a class="ref" href="normsp_1.html#T8">NORMSP_1:8</a>, <a class="ref" href="xxreal_0.html#T17">XXREAL_0:17</a></i>;<br/>
<a NAME="E32:8_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p2">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;=</a> <span class="p1">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span> <a href="real_1.html#K4">*</a> <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><font color="Maroon">c<sub>5</sub></font></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="E33:8_1_2_1_1"/><b>then </b>
<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"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p0">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p0">(<span class="default"><span class="p1">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>14</sub></font>
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E28:8_1_2_1_1"><i><font color="Green">E28</font></i></a>, <a class="txt" href="ndiff_2.html#E30:8_1_2_1_1"><i><font color="Green">E29</font></i></a>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>
<a NAME="E34:8_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">{<span class="default"> <font color="Olive">b<sub>1</sub></font> where B is   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font> : <span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>14</sub></font> </span>}</span> 
 
;<br/>
<a NAME="E35:8_1_2_1_1"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>13</sub></font>
 
<b>by </b><i><a class="txt" href="ndiff_2.html#E4:8_1_2_1_1"><i><font color="Green">E18</font></i></a></i>;<br/>
<b>hence </b><a NAME="E36:8_1_2_1_1"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font> &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="square_1.html#K1">min</a> <span class="p3">(<span class="default">1 <a href="real_1.html#K6">/</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>16</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span>,<span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="square_1.html#K1">min</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> <a href="real_1.html#K6">/</a> 2</span>)</span></span>)</span> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="ndiff_2.html#E2:8_1_2_1_1"><i><font color="Green">E17</font></i></a></i>;<br/>


</div><b>end;</b></div><b>consider </b><font color="Maroon">c<sub>13</sub></font> being   <a href="real_1.html#NM1">Real</a><b> such that </b><br/><a NAME="E11:8_1_2_1"/><i><font color="Green">E17</font></i>: 
(  <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>13</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>11</sub></font> &amp;  <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>13</sub></font> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> 0 &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>8</sub></font> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>9</sub></font> )
 <b>by </b><i><a class="txt" href="ndiff_2.html#E9:8_1_2_1"><i><font color="Green">E16</font></i></a></i>;<br/><a NAME="E12:8_1_2_1"/><i><font color="Green">E18</font></i>: 
<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"><span class="p4">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>6</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K6">/</a> 2
 <b>by </b><i><a class="txt" href="ndiff_2.html#E5:8_1_2_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="ndiff_2.html#E11:8_1_2_1"><i><font color="Green">E17</font></i></a></i>;<br/><a NAME="E13:8_1_2_1"/><i><font color="Green">E19</font></i>: 
<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"><span class="p4">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K6">/</a> 2
 <b>by </b><i><a class="txt" href="ndiff_2.html#E8:8_1_2_1"><i><font color="Green">E15</font></i></a>, <a class="txt" href="ndiff_2.html#E11:8_1_2_1"><i><font color="Green">E17</font></i></a></i>;<br/><a NAME="E14:8_1_2_1"/>
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K6">-</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="real_1.html#K2">"</a> </span>)</span> <a href="rlvect_1.html#K3">*</a> <span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <span class="p0">(<span class="default"><span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>5</sub></font></span>)</span> <a href="rlvect_1.html#K4">+</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span> <a href="rlvect_1.html#K6">-</a> <span class="p5">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="finseq_4.html#K4">/.</a> <font color="Maroon">c<sub>4</sub></font></span>)</span></span>)</span></span>)</span></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font> <a href="real_1.html#K6">/</a> 2
 <b>by </b><i><a class="txt" href="ndiff_2.html#E12:8_1_2_1"><i><font color="Green">E18</font></i></a>, <a class="ref" href="ndiff_2.html#T4" target="_self">Th4</a></i>;<br/><b>hence </b><a NAME="E15:8_1_2_1"/>
<span class="p1"><a href="normsp_1.html#K1">||.</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>6</sub></font> <a href="rlvect_1.html#K6">-</a> <font color="Maroon">c<sub>7</sub></font></span>)</span></span><a href="normsp_1.html#K1">.||</a></span> <a href="xxreal_0.html#R1">&lt;</a> <font color="Maroon">c<sub>10</sub></font>
 <b>by </b><i><a class="txt" href="ndiff_2.html#E1:8_1_2_1"><i><font color="Green">E10</font></i></a>, <a class="txt" href="ndiff_2.html#E13:8_1_2_1"><i><font color="Green">E19</font></i></a>, <a class="ref" href="ndiff_2.html#T4" target="_self">Th4</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E10:8_1_2"/>
<font color="Maroon">c<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font>
 <b>by </b><i><a class="ref" href="ndiff_2.html#T4" target="_self">Th4</a></i>;<br/>


</div>
