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<div>:: <span class="kw">deftheorem </span><span class="lab"><font color="Green" title="E30">Def7</font></span>   defines <a href="jordan3.html#K4" title="JORDAN3:func.4">B_Cut</a> <a onclick="hs(this)" href="javascript:()">JORDAN3:def 7 : <br/></a><span> for <font color="Olive" title="b1">f</font> being   <a href="struct_0.html#NM7" title="STRUCT_0:NM.7">FinSequence</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span><br/>  for <font color="Olive" title="b2">p</font>, <font color="Olive" title="b3">q</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> holds <br/> ( ( ( ( <font color="Olive" title="b2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b3">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Olive" title="b1">f</font> &amp;  <a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b1">f</font>) ) or (  <a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b1">f</font>) &amp;  <a href="jordan3.html#R2" title="JORDAN3:pred.2">LE</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font>,<font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font>)</span>)</span>,<font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> ) ) implies  <a href="jordan3.html#K4" title="JORDAN3:func.4">B_Cut</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan3.html#K3" title="JORDAN3:func.3">R_Cut</a> (<span class="p1">(<span class="default"><a href="jordan3.html#K2" title="JORDAN3:func.2">L_Cut</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">p</font>)</span>)</span>,<font color="Olive" title="b3">q</font>) ) &amp; ( ( <font color="Olive" title="b2">p</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Olive" title="b1">f</font> &amp; <font color="Olive" title="b3">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Olive" title="b1">f</font> &amp;  <a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font>) <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b1">f</font>) ) or (  <a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b3">q</font>,<font color="Olive" title="b1">f</font>) &amp;  <a href="jordan3.html#R2" title="JORDAN3:pred.2">LE</a> <font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font>,<font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font>)</span>)</span>,<font color="Olive" title="b1">f</font> <a href="partfun1.html#K7" title="PARTFUN1:func.7">/.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan3.html#K1" title="JORDAN3:func.1">Index</a> (<font color="Olive" title="b2">p</font>,<font color="Olive" title="b1">f</font>)</span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> ) or  <a href="jordan3.html#K4" title="JORDAN3:func.4">B_Cut</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b2">p</font>,<font color="Olive" title="b3">q</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_5.html#K4" title="FINSEQ_5:func.4">Rev</a> <span class="p1">(<span class="default"><a href="jordan3.html#K3" title="JORDAN3:func.3">R_Cut</a> (<span class="p2">(<span class="default"><a href="jordan3.html#K2" title="JORDAN3:func.2">L_Cut</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b3">q</font>)</span>)</span>,<font color="Olive" title="b2">p</font>)</span>)</span> ) );<br/></span></div>
