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<span class="kw">let </span><font color="Maroon" title="c1">s</font> be   <a href="ami_2.html#NM1" title="AMI_2:NM.1">SCM-State</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">t</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> <br/> for <font color="Olive" title="b2">u</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/> for <font color="Olive" title="b3">mk</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>   st <font color="Olive" title="b3">mk</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b1">t</font> holds <br/><span class="p1">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c1">s</font>,<font color="Olive" title="b1">t</font>,<font color="Olive" title="b2">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">mk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b3">mk</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">t</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">u</font> being  <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a><br/> for <font color="Olive" title="b2">mk</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>   st <font color="Olive" title="b2">mk</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">t</font> holds <br/><span class="p1">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>,<font color="Olive" title="b1">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">mk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">mk</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">u</font> be   <a href="int_1.html#NM1" title="INT_1:NM.1">Integer</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">mk</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a>   st <font color="Olive" title="b1">mk</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">t</font> holds <br/><span class="p1">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c3">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">mk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">mk</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">mk</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K4" title="AMI_2:func.4">SCM-Data-Loc</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">mk</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">t</font> implies <span class="p1">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c3">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">mk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">mk</font> )</span><br/>







<span class="kw">assume </span><a NAME="E1:37"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<font color="Maroon" title="c4">mk</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c2">t</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c3">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">mk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">mk</font></span><br/>

<a NAME="E2:37"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">t</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">t</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c3">u</font></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/>
<a NAME="E3:37"/><span class="kw">then </span>
not <font color="Maroon" title="c4">mk</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"><font color="Maroon" title="c2">t</font> <a href="funcop_1.html#K16" title="FUNCOP_1:func.16">.--&gt;</a> <font color="Maroon" title="c3">u</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:37"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:37"/>
<span class="p1">(<span class="default"><a href="ami_2.html#K10" title="AMI_2:func.10">SCM-Chg</a> <font color="Maroon" title="c1">s</font>,<font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c3">u</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">mk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">s</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">mk</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</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/>


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