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<span class="kw">thus </span><a NAME="E1:34_1_1"/>
 <a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">E</font> is  <a href="ami_1.html#V5" title="AMI_1:attr.5">IC-Ins-separated</a> 
  <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">E</font> is  <a href="ami_1.html#V8" title="AMI_1:attr.8">definite</a> </span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1_1"><span class="kw">proof </span></a><div class="add">

<a NAME="E1:34_1_1_1"/>
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<a NAME="E2:34_1_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E9">A1</font></span>: 
 <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<a NAME="E3:34_1_1_1"/>
 <a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D2" target="_self" title="AMI_1:def.2">Def2</a></span>;<br/>
<span class="kw">hence </span> <a href="ami_1.html#K3" title="AMI_1:func.3">ObjectKind</a> <span class="p1">(<span class="default"><a href="ami_1.html#K2" title="AMI_1:func.2">IC</a> <span class="p2">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">E</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D2" target="_self" title="AMI_1:def.2">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34_1_1_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a>, <a class="ref" href="funct_4.html#T14" title="FUNCT_4:th.14">FUNCT_4:14</a></span>
<br/>.= 
 <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T87" title="FUNCOP_1:th.87">FUNCOP_1:87</a></span>
;<br/> <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ami_1.html#D11" target="_self" title="AMI_1:def.11">AMI_1:def 11</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c2">l</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="ami_1.html#D14" target="_self" title="AMI_1:def.14">AMI_1:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">E</font></span>)</span></span><br/>

<a NAME="E2:34_1_1"/><span class="lab"><font color="Green" title="E9">A1</font></span>: 
<font color="Maroon" title="c2">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_1_2"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:34_1_1_2"/>
<font color="Maroon" title="c2">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> contradiction</span><br/><a NAME="E2:34_1_1_2"/><span class="kw">then </span>
<font color="Maroon" title="c2">l</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/><span class="kw">hence </span><a NAME="E3:34_1_1_2"/>
contradiction
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:34_1_1"><span class="lab"><font color="Green" title="E9">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<a NAME="E4:34_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E10">A2</font></span>: 
not <font color="Maroon" title="c2">l</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></span>;<br/>
<span class="kw">thus </span>the <a href="ami_1.html#U3" title="AMI_1:sel.3">Object-Kind</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">E</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">l</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p3"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p4"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p2">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> </span>)</span></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c2">l</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D2" target="_self" title="AMI_1:def.2">Def2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a> <span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p3"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">l</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:34_1_1"><span class="lab"><font color="Green" title="E10">A2</font></span></a>, <a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></span>
<br/>.= 
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><a href="numbers.html#K6" title="NUMBERS:func.6">0</a> ,<a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> </span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funcop_1.html#T13" title="FUNCOP_1:th.13">FUNCOP_1:13</a></span>
<br/>.= 
the <a href="ami_1.html#U2" title="AMI_1:sel.2">Instructions</a> of <span class="p1">(<span class="default"><a href="ami_1.html#K1" title="AMI_1:func.1">Trivial-AMI</a> <font color="Maroon" title="c1">E</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="ami_1.html#D2" target="_self" title="AMI_1:def.2">Def2</a></span>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
