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<b>let </b><font color="Maroon" title="c1">s</font> be   <a href="scmfsa_1.html#NM1" title="SCMFSA_1:NM.1">SCM+FSA-State</a>; <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">t</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a> <br/> for <font color="Olive" title="b2">u</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</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="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-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="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-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="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</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="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <font color="Olive" title="b3">mk</font></span><br/><b>let </b><font color="Maroon" title="c2">t</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a> ; <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">u</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</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="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-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="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-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="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</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="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <font color="Olive" title="b2">mk</font></span><br/><b>let </b><font color="Maroon" title="c3">u</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ; <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">mk</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-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="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-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="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</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="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <font color="Olive" title="b1">mk</font></span><br/><b>let </b><font color="Maroon" title="c4">mk</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-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="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</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="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <font color="Maroon" title="c4">mk</font> )</span><br/>







<b>assume </b><a NAME="E1:54"/><i><font color="Green" title="E17">A1</font></i>: 
<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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-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="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</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="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <font color="Maroon" title="c4">mk</font></span><br/>

<a NAME="E2:54"/>
<span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">t</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</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>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<a NAME="E3:54"/><b>then </b>
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>
 
<b>by </b><i><a class="txt" href="#E1:54"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></i>;<br/>
<b>hence </b><a NAME="E4:54"/>
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K10" title="SCMFSA_1:func.10">SCM+FSA-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="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</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="scmfsa_1.html#K12" title="SCMFSA_1:func.12">.</a> <font color="Maroon" title="c4">mk</font>
 <b>by </b><i><a class="ref" href="funct_4.html#T12" title="FUNCT_4:th.12">FUNCT_4:12</a></i>; <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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