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<b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="ami_1.html#NM1">Object</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="ami_7.html#D2" target="_self">AMI_7:def 2</a><br/>

<a NAME="E1:10_1_1"/><i><font color="Green">E10</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <a href="numbers.html#K5">NAT</a>  <a href="xboole_0.html#K2">\/</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="amistd_1.html#D11">AMISTD_1:def 11</a></i>;<br/>
<a NAME="E2:10_1_1"/><i><font color="Green">E11</font></i>: 
the <a href="ami_1.html#U5">Object-Kind</a> of <span class="p1">(<span class="default"><a href="amistd_1.html#K4">STC</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p2"><a href="tarski.html#K2">{</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default">1,0</span><a href="tarski.html#K4">]</a></span>,<span class="p3"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span></span>)</span> <a href="funct_4.html#K1">+*</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="amistd_1.html#D11">AMISTD_1:def 11</a></i>;<br/>
<a NAME="E3:10_1_1"/><i><font color="Green">E12</font></i>: 
 <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="tarski.html#K1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19">FUNCOP_1:19</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:10_1_1_1"/>
( <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a>  or <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="tarski.html#K1">}</a></span> )
 </span><b>by </b><i><a class="txt" href="ami_7.html#E1:10_1_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1_1_1"><b>suppose </b></a><a NAME="E1:10_1_1_1_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="numbers.html#K5">NAT</a> 
 ;<br/><div class="add"><a NAME="E2:10_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="numbers.html#K5">NAT</a> 
 ;<br/><a NAME="E3:10_1_1_1_1"/><b>then </b>
not <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span>
 <b>by </b><i><a class="txt" href="ami_7.html#E3:10_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><b>then </b><i><font color="Green">E14</font></i>:  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="funcop_1.html#K2">--&gt;</a> <span class="p2"><a href="tarski.html#K2">{</a><span class="default"><span class="p3"><a href="tarski.html#K4">[</a><span class="default">1,0</span><a href="tarski.html#K4">]</a></span>,<span class="p3"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="ami_7.html#E2:10_1_1"><i><font color="Green">E11</font></i></a>, <a class="ref" href="funct_4.html#T12">FUNCT_4:12</a></i>
<br/>.= 
<span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default">1,0</span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span>
<b>by </b><i><a class="txt" href="ami_7.html#E1:10_1_1_1_1"><i><font color="Green">E13</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/><a NAME="E5:10_1_1_1_1"/><i><font color="Green">E15</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default">1,0</span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T33">ZFMISC_1:33</a></i>;<br/><a NAME="E6:10_1_1_1_1"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default">1,0</span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default">1,0</span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> &amp; <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K2">{</a><span class="default"><span class="p2"><a href="tarski.html#K4">[</a><span class="default">1,0</span><a href="tarski.html#K4">]</a></span>,<span class="p2"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span></span><a href="tarski.html#K2">}</a></span> )
 <b>by </b><i><a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>hence </b><a NAME="E7:10_1_1_1_1"/>
not  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">c<sub>2</sub></font> is <a href="realset1.html#V1">trivial</a>
 <b>by </b><i><a class="txt" href="ami_7.html#E4:10_1_1_1_1"><i><font color="Green">E14</font></i></a>, <a class="txt" href="ami_7.html#E5:10_1_1_1_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="yellow_8.html#D1">YELLOW_8:def 1</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_1_1_1_2"><b>suppose </b></a><a NAME="E1:10_1_1_1_2"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="tarski.html#K1">{</a><span class="default"><a href="numbers.html#K5">NAT</a> </span><a href="tarski.html#K1">}</a></span>
 ;<br/><div class="add"><b>then </b> <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">c<sub>2</sub></font> = 
<span class="p1">(<span class="default"><a href="numbers.html#K5">NAT</a>  <a href="cqc_lang.html#K3">.--&gt;</a> <a href="numbers.html#K5">NAT</a> </span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">c<sub>2</sub></font>
<b>by </b><i><a class="txt" href="ami_7.html#E2:10_1_1"><i><font color="Green">E11</font></i></a>, <a class="txt" href="ami_7.html#E3:10_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="funct_4.html#T14">FUNCT_4:14</a></i>
<br/>.= 
 <a href="numbers.html#K5">NAT</a> 
<b>by </b><i><a class="txt" href="ami_7.html#E1:10_1_1_1_2"><i><font color="Green">E13</font></i></a>, <a class="ref" href="funcop_1.html#T13">FUNCOP_1:13</a></i>
;<br/><b>hence </b><a NAME="E3:10_1_1_1_2"/>
not  <a href="ami_1.html#K3">ObjectKind</a> <font color="Maroon">c<sub>2</sub></font> is <a href="realset1.html#V1">trivial</a>
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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