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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">s</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b3">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="b4">f</font>, <font color="Olive" title="b5">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="b3">BASSIGN</font></span>)</span> holds <br/> ( <font color="Olive" title="b2">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b4">f</font> <a href="modelc_1.html#K30" title="MODELC_1:func.30">'or'</a> <font color="Olive" title="b5">g</font> iff ( <font color="Olive" title="b2">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b4">f</font> or <font color="Olive" title="b2">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b5">g</font> ) )</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">s</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <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="Maroon" title="c2">R</font>,<font color="Olive" title="b2">BASSIGN</font></span>)</span> holds <br/> ( <font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b3">f</font> <a href="modelc_1.html#K30" title="MODELC_1:func.30">'or'</a> <font color="Olive" title="b4">g</font> iff ( <font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b3">f</font> or <font color="Olive" title="b1">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b4">g</font> ) )</span><br/><b>let </b><font color="Maroon" title="c3">s</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</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"> 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> holds <br/> ( <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b2">f</font> <a href="modelc_1.html#K30" title="MODELC_1:func.30">'or'</a> <font color="Olive" title="b3">g</font> iff ( <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b2">f</font> or <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b3">g</font> ) )</span><br/><b>let </b><font color="Maroon" title="c4">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="c4">BASSIGN</font></span>)</span> holds <br/> ( <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b1">f</font> <a href="modelc_1.html#K30" title="MODELC_1:func.30">'or'</a> <font color="Olive" title="b2">g</font> iff ( <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b1">f</font> or <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Olive" title="b2">g</font> ) )</span><br/><b>let </b><font color="Maroon" title="c5">f</font>, <font color="Maroon" title="c6">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="c4">BASSIGN</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c5">f</font> <a href="modelc_1.html#K30" title="MODELC_1:func.30">'or'</a> <font color="Maroon" title="c6">g</font> iff ( <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c5">f</font> or <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c6">g</font> ) )</span><br/>









<a NAME="E1:130"/>
( <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c5">f</font> <a href="modelc_1.html#K30" title="MODELC_1:func.30">'or'</a> <font color="Maroon" title="c6">g</font> iff not <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K25" title="MODELC_1:func.25">'not'</a> <font color="Maroon" title="c5">f</font></span>)</span> <a href="modelc_1.html#K26" title="MODELC_1:func.26">'&amp;'</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K25" title="MODELC_1:func.25">'not'</a> <font color="Maroon" title="c6">g</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="modelc_1.html#T12" target="_self" title="MODELC_1:th.12">Th12</a></i>;<br/>
<a NAME="E2:130"/><b>then </b>
( <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c5">f</font> <a href="modelc_1.html#K30" title="MODELC_1:func.30">'or'</a> <font color="Maroon" title="c6">g</font> iff (  not <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K25" title="MODELC_1:func.25">'not'</a> <font color="Maroon" title="c5">f</font> or  not <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a>  <a href="modelc_1.html#K25" title="MODELC_1:func.25">'not'</a> <font color="Maroon" title="c6">g</font> ) )
 
<b>by </b><i><a class="ref" href="modelc_1.html#T13" target="_self" title="MODELC_1:th.13">Th13</a></i>;<br/>
<b>hence </b><a NAME="E3:130"/>
( <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c5">f</font> <a href="modelc_1.html#K30" title="MODELC_1:func.30">'or'</a> <font color="Maroon" title="c6">g</font> iff ( <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c5">f</font> or <font color="Maroon" title="c3">s</font> <a href="modelc_1.html#R3" title="MODELC_1:pred.3">|=</a> <font color="Maroon" title="c6">g</font> ) )
 <b>by </b><i><a class="ref" href="modelc_1.html#T12" target="_self" title="MODELC_1:th.12">Th12</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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