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<span class="kw">let </span><font color="Maroon" title="c1">I</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">A</font> being  <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font><br/> for <font color="Olive" title="b2">B</font> being <a href="relat_1.html#V2" title="RELAT_1:attr.2">V8</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>  st <font color="Olive" title="b1">A</font> is    <a href="pboole.html#M1" title="PBOOLE:mode.1">Element</a> of <font color="Olive" title="b2">B</font> holds <br/><font color="Olive" title="b1">A</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Olive" title="b2">B</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">A</font> be   <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</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">B</font> being <a href="relat_1.html#V2" title="RELAT_1:attr.2">V8</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>  st <font color="Maroon" title="c2">A</font> is    <a href="pboole.html#M1" title="PBOOLE:mode.1">Element</a> of <font color="Olive" title="b1">B</font> holds <br/><font color="Maroon" title="c2">A</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Olive" title="b1">B</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">B</font> be  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V8</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c1">I</font>; <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="c2">A</font> is    <a href="pboole.html#M1" title="PBOOLE:mode.1">Element</a> of <font color="Maroon" title="c3">B</font> implies <font color="Maroon" title="c2">A</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Maroon" title="c3">B</font> )</span><br/>





<span class="kw">assume </span><a NAME="E1:16"/><span class="lab"><font color="Green" title="E2">A1</font></span>: 
<font color="Maroon" title="c2">A</font> is    <a href="pboole.html#M1" title="PBOOLE:mode.1">Element</a> of <font color="Maroon" title="c3">B</font>
 ; <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="c2">A</font> <a href="pboole.html#R1" title="PBOOLE:pred.1">in</a> <font color="Maroon" title="c3">B</font></span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="pboole.html#D4" title="PBOOLE:def.4">PBOOLE:def 4</a> <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="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font> or <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:16"/><span class="lab"><font color="Green" title="E3">A2</font></span>: 
<font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">I</font>
 ; <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="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span><br/>

<a NAME="E3:16"/><span class="kw">then </span><span class="lab"><font color="Green" title="E4">A3</font></span>: 
<font color="Maroon" title="c3">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
;<br/>
<a NAME="E4:16"/>
<font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> is    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c3">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:16"><span class="lab"><font color="Green" title="E2">A1</font></span></a>, <a class="txt" href="#E2:16"><span class="lab"><font color="Green" title="E3">A2</font></span></a>, <a class="ref" href="pboole.html#D17" title="PBOOLE:def.17">PBOOLE:def 17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E5:16"/>
<font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">B</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:16"><span class="lab"><font color="Green" title="E4">A3</font></span></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/>


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