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<span class="kw">let </span><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:()"><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="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-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">f</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>  holds  <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">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">f</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">f</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="scmfsa_1.html#K3" title="SCMFSA_1:func.3">SCM+FSA-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">f</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>  holds  <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">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">f</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">f</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">f</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>  holds  <span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">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">f</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">f</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="scmfsa_1.html#K4" title="SCMFSA_1:func.4">SCM+FSA-Data*-Loc</a> ; <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="scmfsa_1.html#K9" title="SCMFSA_1:func.9">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="E1:54"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<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>
 
<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="E2:54"/>
( <a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  &amp; <a href="scmfsa_1.html#K7" title="SCMFSA_1:func.7">SCM+FSA-OK</a>  <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">mk</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  <a href="finseq_2.html#K3" title="FINSEQ_2:func.3">*</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scmfsa_1.html#T10" target="_self" title="SCMFSA_1:th.10">Th10</a>, <a class="ref" href="scmfsa_1.html#T12" target="_self" title="SCMFSA_1:th.12">Th12</a></span>;<br/>
<a NAME="E3:54"/><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="#E1:54"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="ref" href="funct_7.html#T18" title="FUNCT_7:th.18">FUNCT_7:18</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="E4:54"/>
<span class="p1">(<span class="default"><a href="scmfsa_1.html#K9" title="SCMFSA_1:func.9">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 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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