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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="59_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">n</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</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="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="prob_3.html#K9" title="PROB_3:func.9">Complement</a> <font color="Maroon" title="c3">F</font></span>)</span> implies <span class="p1">(<span class="default"><a href="prob_3.html#K9" title="PROB_3:func.9">Complement</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="prob_3.html#K7" title="PROB_3:func.7">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font> )</span><br/><span class="kw">assume </span><a NAME="E1:59_1_1_1"/>
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="prob_3.html#K9" title="PROB_3:func.9">Complement</a> <font color="Maroon" title="c3">F</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="prob_3.html#K9" title="PROB_3:func.9">Complement</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="prob_3.html#K7" title="PROB_3:func.7">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font></span><br/><a NAME="E2:59_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="prob_3.html#K9" title="PROB_3:func.9">Complement</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="prob_3.html#K7" title="PROB_3:func.7">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">F</font> <a href="prob_3.html#K11" title="PROB_3:func.11">.</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="subset_1.html#K3" title="SUBSET_1:func.3">`</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_3.html#D8" target="_self" title="PROB_3:def.8">Def8</a></span>;<br/><a NAME="E3:59_1_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="prob_3.html#K9" title="PROB_3:func.9">Complement</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="prob_3.html#K7" title="PROB_3:func.7">.</a> <font color="Maroon" title="c4">n</font> is    <a href="prob_1.html#M1" title="PROB_1:mode.1">Event</a> of <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_1.html#T50" title="PROB_1:th.50">PROB_1:50</a></span>;<br/><span class="kw">hence </span><a NAME="E4:59_1_1_1"/>
<span class="p1">(<span class="default"><a href="prob_3.html#K9" title="PROB_3:func.9">Complement</a> <font color="Maroon" title="c3">F</font></span>)</span> <a href="prob_3.html#K7" title="PROB_3:func.7">.</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">S</font>
 ; <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">hence </span><a NAME="E2:59_1_1"/>
 <a href="prob_3.html#K9" title="PROB_3:func.9">Complement</a> <font color="Maroon" title="c3">F</font> is    <a href="prob_3.html#M1" title="PROB_3:mode.1">FinSequence</a> of <font color="Maroon" title="c2">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="prob_3.html#D10" target="_self" title="PROB_3:def.10">Def10</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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