<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">S</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</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">V</font> being <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">X</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"><font color="Maroon" title="c1">S</font> <a href="msaterm.html#K1" title="MSATERM:func.1">-Terms</a> <font color="Olive" title="b1">V</font></span>)</span> holds <br/> ( <font color="Olive" title="b2">X</font> is    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">V</font> iff not <font color="Olive" title="b2">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a>  is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V5</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font>; <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">X</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"><font color="Maroon" title="c1">S</font> <a href="msaterm.html#K1" title="MSATERM:func.1">-Terms</a> <font color="Maroon" title="c2">V</font></span>)</span> holds <br/> ( <font color="Olive" title="b1">X</font> is    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font> iff not <font color="Olive" title="b1">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a>  is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">X</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"><font color="Maroon" title="c1">S</font> <a href="msaterm.html#K1" title="MSATERM:func.1">-Terms</a> <font color="Maroon" title="c2">V</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">X</font> is    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font> iff not <font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a>  is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  )</span><br/>





<div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a>  is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  implies <font color="Maroon" title="c3">X</font> is    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font> )</span>
<div class="add"><span class="kw">assume </span><a NAME="E1:4_1"/>
<font color="Maroon" title="c3">X</font> is    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> not <font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a>  is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> </span><br/><span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">t</font> being    <a href="msaterm.html#M2" title="MSATERM:mode.2">CompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font><span class="kw"> such that </span><br/><a NAME="E3:4_1"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<font color="Maroon" title="c4">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msaterm.html#D7" title="MSATERM:def.7">MSATERM:def 7</a></span>;<br/><a NAME="E4:4_1"/>
<font color="Maroon" title="c4">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msaterm.html#D6" title="MSATERM:def.6">MSATERM:def 6</a></span>;<br/><span class="kw">hence </span><a NAME="E5:4_1"/>
not <font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a>  is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:4_1"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="trees_9.html#T26" title="TREES_9:th.26">TREES_9:26</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/></div>
<span class="kw">end;</span></div>

<span class="kw">assume </span><a NAME="E2:4"/>
not <font color="Maroon" title="c3">X</font> <a href="circtrm1.html#K1" title="CIRCTRM1:func.1">-CircuitStr</a>  is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">X</font> is    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c4">t</font> being    <a href="trees_3.html#M3" title="TREES_3:mode.3">Element</a> of <font color="Maroon" title="c3">X</font><span class="kw"> such that </span><br/><a NAME="E4:4"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
(  not <font color="Maroon" title="c4">t</font> is  <a href="zfmisc_1.html#V1" title="ZFMISC_1:attr.1">trivial</a>  or <font color="Maroon" title="c4">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font>,<span class="p2"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="trees_9.html#T26" title="TREES_9:th.26">TREES_9:26</a></span>;<br/>
<a NAME="E5:4"/>
<font color="Maroon" title="c4">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">X</font>
 
;<br/>
<a NAME="E6:4"/><span class="kw">then </span>
<font color="Maroon" title="c4">t</font> is    <a href="msaterm.html#M2" title="MSATERM:mode.2">CompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:4"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="ref" href="msaterm.html#T28" title="MSATERM:th.28">MSATERM:28</a>, <a class="ref" href="msaterm.html#D6" title="MSATERM:def.6">MSATERM:def 6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:4"/>
<font color="Maroon" title="c3">X</font> is    <a href="msaterm.html#M3" title="MSATERM:mode.3">SetWithCompoundTerm</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">V</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="msaterm.html#D7" title="MSATERM:def.7">MSATERM:def 7</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/>


</div>
