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<div><span class="kw">theorem </span><a NAME="T12"><span class="comment"><font color="firebrick">:: TOPREAL1:12</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">n</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a><br/>  for <font color="Olive" title="b2">p1</font>, <font color="Olive" title="b3">p2</font>, <font color="Olive" title="b4">q1</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> <font color="Olive" title="b1">n</font></span>)</span>  st ( <font color="Olive" title="b2">p1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b3">p2</font> or <font color="Olive" title="b3">p2</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Olive" title="b4">q1</font> ) &amp; <span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>)</span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b3">p2</font>,<font color="Olive" title="b4">q1</font>)</span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Olive" title="b3">p2</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span> holds <br/><span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b2">p1</font>,<font color="Olive" title="b3">p2</font>)</span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> (<font color="Olive" title="b3">p2</font>,<font color="Olive" title="b4">q1</font>)</span>)</span> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Olive" title="b2">p1</font>,<font color="Olive" title="b4">q1</font></div></div>
