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<span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#NM1" title="RELSET_1:NM.1">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#K31" title="MODELC_1:func.31">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#K49" title="MODELC_1:func.49">BASSModel</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#K62" title="MODELC_1:func.62">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#K52" title="MODELC_1:func.52">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#K52" title="MODELC_1:func.52">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#K51" title="MODELC_1:func.51">Pred</a> (<font color="Olive" title="b5">X</font>,<font color="Olive" title="b1">R</font>)</span>)</span></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c2">R</font> be   <a href="partfun1.html#V1" title="PARTFUN1:attr.1">total</a>  <a href="relset_1.html#NM1" title="RELSET_1:NM.1">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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K31" title="MODELC_1:func.31">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#K49" title="MODELC_1:func.49">BASSModel</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#K62" title="MODELC_1:func.62">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#K52" title="MODELC_1:func.52">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#K52" title="MODELC_1:func.52">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#K51" title="MODELC_1:func.51">Pred</a> (<font color="Olive" title="b4">X</font>,<font color="Maroon" title="c2">R</font>)</span>)</span></span>)</span></span><br/><span class="kw">let </span><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#K31" title="MODELC_1:func.31">ModelSP</a> <font color="Maroon" title="c1">S</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K49" title="MODELC_1:func.49">BASSModel</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#K62" title="MODELC_1:func.62">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#K52" title="MODELC_1:func.52">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#K52" title="MODELC_1:func.52">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#K51" title="MODELC_1:func.51">Pred</a> (<font color="Olive" title="b3">X</font>,<font color="Maroon" title="c2">R</font>)</span>)</span></span>)</span></span><br/><span class="kw">let </span><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#K49" title="MODELC_1:func.49">BASSModel</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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></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#K62" title="MODELC_1:func.62">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#K52" title="MODELC_1:func.52">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#K52" title="MODELC_1:func.52">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#K51" title="MODELC_1:func.51">Pred</a> (<font color="Olive" title="b1">X</font>,<font color="Maroon" title="c2">R</font>)</span>)</span></span>)</span></span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="modelc_1.html#K62" title="MODELC_1:func.62">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#K52" title="MODELC_1:func.52">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#K52" title="MODELC_1:func.52">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#K51" title="MODELC_1:func.51">Pred</a> (<font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c2">R</font>)</span>)</span></span>)</span></span><br/>









<span class="kw">set </span><font color="Maroon" title="c7">h</font> =  <a href="modelc_1.html#K53" title="MODELC_1:func.53">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#K62" title="MODELC_1:func.62">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#K61" title="MODELC_1:func.61">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>)
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D73" target="_self" title="MODELC_1:def.73">Def75</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="modelc_1.html#K52" title="MODELC_1:func.52">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#K52" title="MODELC_1:func.52">SIGMA</a> <span class="p2">(<span class="default"><a href="modelc_1.html#K54" title="MODELC_1:func.54">Fax</a> (<font color="Maroon" title="c4">f</font>,<span class="p3">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">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 class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#T33" target="_self" title="MODELC_1:th.33">Th33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="modelc_1.html#K52" title="MODELC_1:func.52">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#K52" title="MODELC_1:func.52">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">SIGMA</a> <span class="p3">(<span class="default"><a href="modelc_1.html#K26" title="MODELC_1:func.26">EX</a> <span class="p4">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#T33" target="_self" title="MODELC_1:th.33">Th33</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="modelc_1.html#K52" title="MODELC_1:func.52">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#K52" title="MODELC_1:func.52">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#K51" title="MODELC_1:func.51">Pred</a> (<span class="p3">(<span class="default"><a href="modelc_1.html#K52" title="MODELC_1:func.52">SIGMA</a> <span class="p4">(<span class="default"><a href="modelc_1.html#K53" title="MODELC_1:func.53">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>
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#T50" target="_self" title="MODELC_1:th.50">Th50</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E2:184"/>
<span class="p1">(<span class="default"><a href="modelc_1.html#K62" title="MODELC_1:func.62">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#K52" title="MODELC_1:func.52">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#K52" title="MODELC_1:func.52">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#K51" title="MODELC_1:func.51">Pred</a> (<font color="Maroon" title="c6">X</font>,<font color="Maroon" title="c2">R</font>)</span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#T32" target="_self" title="MODELC_1:th.32">Th32</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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