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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">R</font> being <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">BASSIGN</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <font color="Maroon" title="c1">S</font></span>)</span><br/> for <font color="Olive" title="b3">f</font>, <font color="Olive" title="b4">g</font> being  <a href="modelc_1.html#NM2" title="MODELC_1:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K50" title="MODELC_1:func.50">CTLModel</a> <font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">BASSIGN</font></span>)</span><br/> for <font color="Olive" title="b5">X</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> holds  <span class="p1">(<span class="default"><a href="modelc_1.html#K63" title="MODELC_1:func.63">TransEU</a> <font color="Olive" title="b3">f</font>,<font color="Olive" title="b4">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b5">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Olive" title="b4">g</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Olive" title="b3">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K52" title="MODELC_1:func.52">Pred</a> <font color="Olive" title="b5">X</font>,<font color="Olive" title="b1">R</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">R</font> be  <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="relset_1.html#M2" title="RELSET_1:mode.2">Relation</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font>; <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">BASSIGN</font> being non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <font color="Maroon" title="c1">S</font></span>)</span><br/> for <font color="Olive" title="b2">f</font>, <font color="Olive" title="b3">g</font> being  <a href="modelc_1.html#NM2" title="MODELC_1:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K50" title="MODELC_1:func.50">CTLModel</a> <font color="Maroon" title="c2">R</font>,<font color="Olive" title="b1">BASSIGN</font></span>)</span><br/> for <font color="Olive" title="b4">X</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> holds  <span class="p1">(<span class="default"><a href="modelc_1.html#K63" title="MODELC_1:func.63">TransEU</a> <font color="Olive" title="b2">f</font>,<font color="Olive" title="b3">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Olive" title="b3">g</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Olive" title="b2">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K52" title="MODELC_1:func.52">Pred</a> <font color="Olive" title="b4">X</font>,<font color="Maroon" title="c2">R</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">BASSIGN</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K32" title="MODELC_1:func.32">ModelSP</a> <font color="Maroon" title="c1">S</font></span>)</span>; <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">f</font>, <font color="Olive" title="b2">g</font> being  <a href="modelc_1.html#NM2" title="MODELC_1:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K50" title="MODELC_1:func.50">CTLModel</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font></span>)</span><br/> for <font color="Olive" title="b3">X</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> holds  <span class="p1">(<span class="default"><a href="modelc_1.html#K63" title="MODELC_1:func.63">TransEU</a> <font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Olive" title="b2">g</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Olive" title="b1">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K52" title="MODELC_1:func.52">Pred</a> <font color="Olive" title="b3">X</font>,<font color="Maroon" title="c2">R</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">f</font>, <font color="Maroon" title="c5">g</font> be   <a href="modelc_1.html#NM2" title="MODELC_1:NM.2">Assign</a> of <span class="p1">(<span class="default"><a href="modelc_1.html#K50" title="MODELC_1:func.50">CTLModel</a> <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font></span>)</span>; <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">X</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> holds  <span class="p1">(<span class="default"><a href="modelc_1.html#K63" title="MODELC_1:func.63">TransEU</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K52" title="MODELC_1:func.52">Pred</a> <font color="Olive" title="b1">X</font>,<font color="Maroon" title="c2">R</font></span>)</span></span>)</span></span><br/><b>let </b><font color="Maroon" title="c6">X</font> be   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of <font color="Maroon" title="c1">S</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="modelc_1.html#K63" title="MODELC_1:func.63">TransEU</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K52" title="MODELC_1:func.52">Pred</a> <font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c2">R</font></span>)</span></span>)</span></span><br/>









<b>set </b><font color="Maroon" title="c7">h</font> =  <a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>;<br/>
<span class="p1">(<span class="default"><a href="modelc_1.html#K63" title="MODELC_1:func.63">TransEU</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">X</font> = 
 <a href="modelc_1.html#K62" title="MODELC_1:func.62">SigFoaxTau</a> <font color="Maroon" title="c5">g</font>,<font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font>
<b>by </b><i><a class="ref" href="modelc_1.html#D73" target="_self" title="MODELC_1:def.73">Def73</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K55" title="MODELC_1:func.55">Fax</a> <font color="Maroon" title="c4">f</font>,<span class="p3">(<span class="default"><a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="modelc_1.html#T33" target="_self" title="MODELC_1:th.33">Th33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <span class="p3">(<span class="default"><a href="modelc_1.html#K27" title="MODELC_1:func.27">EX</a> <span class="p4">(<span class="default"><a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font></span>)</span></span>)</span></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="modelc_1.html#T33" target="_self" title="MODELC_1:th.33">Th33</a></i>
<br/>.= 
<span class="p1">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K52" title="MODELC_1:func.52">Pred</a> <span class="p3">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <span class="p4">(<span class="default"><a href="modelc_1.html#K54" title="MODELC_1:func.54">Tau</a> <font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">BASSIGN</font></span>)</span></span>)</span>,<font color="Maroon" title="c2">R</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="modelc_1.html#T50" target="_self" title="MODELC_1:th.50">Th50</a></i>
;<br/>
<b>hence </b><a NAME="E2:182"/>
<span class="p1">(<span class="default"><a href="modelc_1.html#K63" title="MODELC_1:func.63">TransEU</a> <font color="Maroon" title="c4">f</font>,<font color="Maroon" title="c5">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Maroon" title="c5">g</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">SIGMA</a> <font color="Maroon" title="c4">f</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K52" title="MODELC_1:func.52">Pred</a> <font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c2">R</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="modelc_1.html#T32" target="_self" title="MODELC_1:th.32">Th32</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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