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<span class="kw">let </span><font color="Maroon" title="c1">H</font> be   <a href="modelc_1.html#NM1" title="MODELC_1:NM.1">CTL-formula</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">S</font> being   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> <br/>  for <font color="Olive" title="b2">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="Olive" title="b1">S</font>,<font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b4">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="Olive" title="b1">S</font></span>)</span><br/>  for <font color="Olive" title="b5">kai</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a>, the <a href="modelc_1.html#U3" title="MODELC_1:sel.3">BasicAssign</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="b2">R</font>,<font color="Olive" title="b4">BASSIGN</font>)</span>)</span>  st <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  holds <br/>( <font color="Olive" title="b3">s</font>,<font color="Olive" title="b5">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Olive" title="b5">kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K47" title="MODELC_1:func.47">Label_</a> <font color="Olive" title="b4">BASSIGN</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">s</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">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="c2">S</font>,<font color="Maroon" title="c2">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="c2">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#K31" title="MODELC_1:func.31">ModelSP</a> <font color="Maroon" title="c2">S</font></span>)</span><br/>  for <font color="Olive" title="b4">kai</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a>, the <a href="modelc_1.html#U3" title="MODELC_1:sel.3">BasicAssign</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="b3">BASSIGN</font>)</span>)</span>  st <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  holds <br/>( <font color="Olive" title="b2">s</font>,<font color="Olive" title="b4">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Olive" title="b4">kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K47" title="MODELC_1:func.47">Label_</a> <font color="Olive" title="b3">BASSIGN</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">s</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">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="c2">S</font>,<font color="Maroon" title="c2">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">s</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">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="c2">S</font></span>)</span><br/>  for <font color="Olive" title="b3">kai</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a>, the <a href="modelc_1.html#U3" title="MODELC_1:sel.3">BasicAssign</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="c3">R</font>,<font color="Olive" title="b2">BASSIGN</font>)</span>)</span>  st <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  holds <br/>( <font color="Olive" title="b1">s</font>,<font color="Olive" title="b3">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Olive" title="b3">kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K47" title="MODELC_1:func.47">Label_</a> <font color="Olive" title="b2">BASSIGN</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">s</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c4">s</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c2">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="c2">S</font></span>)</span><br/>  for <font color="Olive" title="b2">kai</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a>, the <a href="modelc_1.html#U3" title="MODELC_1:sel.3">BasicAssign</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="c3">R</font>,<font color="Olive" title="b1">BASSIGN</font>)</span>)</span>  st <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  holds <br/>( <font color="Maroon" title="c4">s</font>,<font color="Olive" title="b2">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Olive" title="b2">kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K47" title="MODELC_1:func.47">Label_</a> <font color="Olive" title="b1">BASSIGN</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c5">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="c2">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">kai</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a>, the <a href="modelc_1.html#U3" title="MODELC_1:sel.3">BasicAssign</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="c3">R</font>,<font color="Maroon" title="c5">BASSIGN</font>)</span>)</span>  st <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  holds <br/>( <font color="Maroon" title="c4">s</font>,<font color="Olive" title="b1">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Olive" title="b1">kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K47" title="MODELC_1:func.47">Label_</a> <font color="Maroon" title="c5">BASSIGN</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c6">kai</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a>, the <a href="modelc_1.html#U3" title="MODELC_1:sel.3">BasicAssign</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="c3">R</font>,<font color="Maroon" title="c5">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"> ( <font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a>  implies ( <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Maroon" title="c6">kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K47" title="MODELC_1:func.47">Label_</a> <font color="Maroon" title="c5">BASSIGN</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s</font> ) )</span><br/>











<span class="kw">assume </span><a NAME="E1:135"/><span class="lab"><font color="Green" title="E101">A1</font></span>: 
<font color="Maroon" title="c1">H</font> is  <a href="modelc_1.html#V2" title="MODELC_1:attr.2">atomic</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Maroon" title="c6">kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K47" title="MODELC_1:func.47">Label_</a> <font color="Maroon" title="c5">BASSIGN</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s</font> )</span><br/>

<a NAME="E2:135"/>
 ex <font color="Olive" title="b1">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <a href="modelc_1.html#K13" title="MODELC_1:func.13">CTL_WFF</a>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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="c3">R</font>,<font color="Maroon" title="c5">BASSIGN</font>)</span>)</span> st <br/>( <font color="Olive" title="b1">f</font> <a href="modelc_1.html#R1" title="MODELC_1:pred.1">is-Evaluation-for</a> <font color="Maroon" title="c6">kai</font> &amp;  <a href="modelc_1.html#K25" title="MODELC_1:func.25">Evaluate</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c6">kai</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">H</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D34" target="_self" title="MODELC_1:def.34">Def34</a></span>;<br/>
<a NAME="E3:135"/><span class="kw">then </span><span class="lab"><font color="Green" title="E102">A2</font></span>: 
 <a href="modelc_1.html#K25" title="MODELC_1:func.25">Evaluate</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c6">kai</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">H</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:135"><span class="lab"><font color="Green" title="E101">A1</font></span></a>, <a class="ref" href="modelc_1.html#D26" target="_self" title="MODELC_1:def.26">Def26</a></span>;<br/>
<a NAME="E4:135"/><span class="lab"><font color="Green" title="E103">A3</font></span>: 
( <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Maroon" title="c4">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">Evaluate</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c6">kai</font>) )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="modelc_1.html#D60" target="_self" title="MODELC_1:def.60">Def62</a></span>;<br/>
<a NAME="E5:135"/>
<font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="modelc_1.html#K19" title="MODELC_1:func.19">atomic_WFF</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:135"><span class="lab"><font color="Green" title="E101">A1</font></span></a></span>;<br/>
<a NAME="E6:135"/><span class="kw">then </span>
 <a href="modelc_1.html#K25" title="MODELC_1:func.25">Evaluate</a> (<font color="Maroon" title="c1">H</font>,<font color="Maroon" title="c6">kai</font>) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">BASSIGN</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:135"><span class="lab"><font color="Green" title="E102">A2</font></span></a>, <a class="ref" href="funct_2.html#T5" title="FUNCT_2:th.5">FUNCT_2:5</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:135"/>
( <font color="Maroon" title="c4">s</font>,<font color="Maroon" title="c6">kai</font> <a href="modelc_1.html#R4" title="MODELC_1:pred.4">|=</a> <font color="Maroon" title="c1">H</font> iff <font color="Maroon" title="c6">kai</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c1">H</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="modelc_1.html#K47" title="MODELC_1:func.47">Label_</a> <font color="Maroon" title="c5">BASSIGN</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">s</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:135"><span class="lab"><font color="Green" title="E102">A2</font></span></a>, <a class="txt" href="#E4:135"><span class="lab"><font color="Green" title="E103">A3</font></span></a>, <a class="ref" href="modelc_1.html#T11" target="_self" title="MODELC_1:th.11">Th11</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/>


</div>
