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<b>set </b><font color="Maroon" title="c2">N</font> =  <a href="metric_1.html#K6" title="METRIC_1:func.6">DiscreteSpace</a> <font color="Maroon" title="c1">A</font>;<br/>
<b>take </b>
2
; <i><font color="Red">:: according to </font></i><a class="ref" href="tbsp_1.html#D8" target="_self" title="TBSP_1:def.8">TBSP_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2 &amp; ( for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="metric_1.html#K6" title="METRIC_1:func.6">DiscreteSpace</a> <font color="Maroon" title="c1">A</font></span>)</span> holds   <a href="metric_1.html#K2" title="METRIC_1:func.2">dist</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 2 ) )</span><br/>

<b>thus </b><a NAME="E1:18_1_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="metric_1.html#K6" title="METRIC_1:func.6">DiscreteSpace</a> <font color="Maroon" title="c1">A</font></span>)</span> holds   <a href="metric_1.html#K2" title="METRIC_1:func.2">dist</a> <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 2</span><br/>

<a NAME="E2:18_1_1"/><i><font color="Green" title="E13">A1</font></i>: 
 <a href="metric_1.html#K6" title="METRIC_1:func.6">DiscreteSpace</a> <font color="Maroon" title="c1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="metric_1.html#G1" title="METRIC_1:aggr.1">MetrStruct</a>(# <font color="Maroon" title="c1">A</font>,<span class="p1">(<span class="default"><a href="metric_1.html#K5" title="METRIC_1:func.5">discrete_dist</a> <font color="Maroon" title="c1">A</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="metric_1.html#D12" title="METRIC_1:def.12">METRIC_1:def 12</a></i>;<br/>
<b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="metric_1.html#K6" title="METRIC_1:func.6">DiscreteSpace</a> <font color="Maroon" title="c1">A</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="metric_1.html#K2" title="METRIC_1:func.2">dist</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 2</span><br/>

<a NAME="E3:18_1_1"/><i><font color="Green" title="E14">A2</font></i>: 
( <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> or <font color="Maroon" title="c3">x</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c4">y</font> )
 
;<br/>
<a NAME="E4:18_1_1"/>
 <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="metric_1.html#U1" title="METRIC_1:sel.1">distance</a> of <span class="p1">(<span class="default"><a href="metric_1.html#K6" title="METRIC_1:func.6">DiscreteSpace</a> <font color="Maroon" title="c1">A</font></span>)</span> <a href="metric_1.html#K1" title="METRIC_1:func.1">.</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font>
 
<b>by </b><i><a class="ref" href="metric_1.html#D1" title="METRIC_1:def.1">METRIC_1:def 1</a></i>;<br/>
<a NAME="E5:18_1_1"/><b>then </b>
(  <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  or  <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 )
 
<b>by </b><i><a class="txt" href="tbsp_1.html#E2:18_1_1"><i><font color="Green" title="E13">A1</font></i></a>, <a class="txt" href="tbsp_1.html#E3:18_1_1"><i><font color="Green" title="E14">A2</font></i></a>, <a class="ref" href="metric_1.html#D11" title="METRIC_1:def.11">METRIC_1:def 11</a></i>;<br/>
<b>hence </b><a NAME="E6:18_1_1"/>
 <a href="metric_1.html#K4" title="METRIC_1:func.4">dist</a> <font color="Maroon" title="c3">x</font>,<font color="Maroon" title="c4">y</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> 2
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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