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<span class="kw">let </span><font color="Maroon" title="c1">P1</font>, <font color="Maroon" title="c2">P2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <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>, <font color="Olive" title="b2">b</font>, <font color="Olive" title="b3">c</font>, <font color="Olive" title="b4">d</font> being  <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> <br/> for <font color="Olive" title="b5">f1</font>, <font color="Olive" title="b6">f2</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="b7">p1</font>, <font color="Olive" title="b8">p2</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>  st <font color="Olive" title="b1">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">b</font> &amp; <font color="Olive" title="b3">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b4">d</font> &amp; <font color="Olive" title="b7">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> &amp; <font color="Olive" title="b8">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> &amp; <font color="Olive" title="b5">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b4">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> &amp; <font color="Olive" title="b6">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Olive" title="b1">a</font>,<font color="Olive" title="b3">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Olive" title="b2">b</font>,<font color="Olive" title="b4">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> &amp; <font color="Maroon" title="c1">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Olive" title="b5">f1</font> &amp; <font color="Maroon" title="c2">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Olive" title="b6">f2</font> holds <br/>( <font color="Maroon" title="c1">P1</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Olive" title="b7">p1</font>,<font color="Olive" title="b8">p2</font> &amp; <font color="Maroon" title="c2">P2</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Olive" title="b7">p1</font>,<font color="Olive" title="b8">p2</font> &amp; not <font color="Maroon" title="c1">P1</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; not <font color="Maroon" title="c2">P2</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  <a href="jgraph_6.html#NK1" title="JGRAPH_6:NK.1">rectangle</a> <font color="Olive" title="b1">a</font>,<font color="Olive" title="b2">b</font>,<font color="Olive" title="b3">c</font>,<font color="Olive" title="b4">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">P1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c2">P2</font> &amp; <font color="Maroon" title="c1">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b7">p1</font>,<font color="Olive" title="b8">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font>, <font color="Maroon" title="c5">c</font>, <font color="Maroon" title="c6">d</font> be   <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</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">f1</font>, <font color="Olive" title="b2">f2</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="b3">p1</font>, <font color="Olive" title="b4">p2</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>  st <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Olive" title="b3">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> &amp; <font color="Olive" title="b4">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> &amp; <font color="Olive" title="b1">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> &amp; <font color="Olive" title="b2">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> &amp; <font color="Maroon" title="c1">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Olive" title="b1">f1</font> &amp; <font color="Maroon" title="c2">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Olive" title="b2">f2</font> holds <br/>( <font color="Maroon" title="c1">P1</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b4">p2</font> &amp; <font color="Maroon" title="c2">P2</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Olive" title="b3">p1</font>,<font color="Olive" title="b4">p2</font> &amp; not <font color="Maroon" title="c1">P1</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; not <font color="Maroon" title="c2">P2</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  <a href="jgraph_6.html#NK1" title="JGRAPH_6:NK.1">rectangle</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">P1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c2">P2</font> &amp; <font color="Maroon" title="c1">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b3">p1</font>,<font color="Olive" title="b4">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c7">f1</font>, <font color="Maroon" title="c8">f2</font> be   <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>; <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">p1</font>, <font color="Olive" title="b2">p2</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>  st <font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Olive" title="b1">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> &amp; <font color="Olive" title="b2">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> &amp; <font color="Maroon" title="c7">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> &amp; <font color="Maroon" title="c8">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> &amp; <font color="Maroon" title="c1">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c7">f1</font> &amp; <font color="Maroon" title="c2">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c8">f2</font> holds <br/>( <font color="Maroon" title="c1">P1</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font> &amp; <font color="Maroon" title="c2">P2</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font> &amp; not <font color="Maroon" title="c1">P1</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; not <font color="Maroon" title="c2">P2</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  <a href="jgraph_6.html#NK1" title="JGRAPH_6:NK.1">rectangle</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">P1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c2">P2</font> &amp; <font color="Maroon" title="c1">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Olive" title="b1">p1</font>,<font color="Olive" title="b2">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )</span><br/><span class="kw">let </span><font color="Maroon" title="c9">p1</font>, <font color="Maroon" title="c10">p2</font> be   <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>; <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">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">b</font> &amp; <font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">d</font> &amp; <font color="Maroon" title="c9">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> &amp; <font color="Maroon" title="c10">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> &amp; <font color="Maroon" title="c7">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> &amp; <font color="Maroon" title="c8">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span> &amp; <font color="Maroon" title="c1">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c7">f1</font> &amp; <font color="Maroon" title="c2">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c8">f2</font> implies ( <font color="Maroon" title="c1">P1</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c10">p2</font> &amp; <font color="Maroon" title="c2">P2</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c10">p2</font> &amp; not <font color="Maroon" title="c1">P1</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; not <font color="Maroon" title="c2">P2</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  <a href="jgraph_6.html#NK1" title="JGRAPH_6:NK.1">rectangle</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">P1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c2">P2</font> &amp; <font color="Maroon" title="c1">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c10">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> ) )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:74"/><span class="lab"><font color="Green" title="E62">A1</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">b</font>
 <span class="kw">and </span><br/><a NAME="E2:74"/><span class="lab"><font color="Green" title="E63">A2</font></span>: 
<font color="Maroon" title="c5">c</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c6">d</font>
 <span class="kw">and </span><br/><a NAME="E3:74"/><span class="lab"><font color="Green" title="E64">A3</font></span>: 
<font color="Maroon" title="c9">p1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>
 <span class="kw">and </span><br/><a NAME="E4:74"/><span class="lab"><font color="Green" title="E65">A4</font></span>: 
<font color="Maroon" title="c10">p2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>
 <span class="kw">and </span><br/><a NAME="E5:74"/><span class="lab"><font color="Green" title="E66">A5</font></span>: 
<font color="Maroon" title="c7">f1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 <span class="kw">and </span><br/><a NAME="E6:74"/><span class="lab"><font color="Green" title="E67">A6</font></span>: 
<font color="Maroon" title="c8">f2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">&lt;*</a><span class="default"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="rlvect_1.html#K6" title="RLVECT_1:func.6">*&gt;</a></span>
 <span class="kw">and </span><br/><a NAME="E7:74"/><span class="lab"><font color="Green" title="E68">A7</font></span>: 
<font color="Maroon" title="c1">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c7">f1</font>
 <span class="kw">and </span><br/><a NAME="E8:74"/><span class="lab"><font color="Green" title="E69">A8</font></span>: 
<font color="Maroon" title="c2">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topreal1.html#K3" title="TOPREAL1:func.3">L~</a> <font color="Maroon" title="c8">f2</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="c1">P1</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c10">p2</font> &amp; <font color="Maroon" title="c2">P2</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c10">p2</font> &amp; not <font color="Maroon" title="c1">P1</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; not <font color="Maroon" title="c2">P2</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  <a href="jgraph_6.html#NK1" title="JGRAPH_6:NK.1">rectangle</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">P1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c2">P2</font> &amp; <font color="Maroon" title="c1">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c10">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )</span><br/>

<a NAME="E9:74"/>
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></span>;<br/>
<a NAME="E10:74"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A9</font></span>: 
( <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> or <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></span>;<br/>
<a NAME="E11:74"/><span class="lab"><font color="Green" title="E71">A10</font></span>: 
<font color="Maroon" title="c1">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></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> <span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="txt" href="#E5:74"><span class="lab"><font color="Green" title="E66">A5</font></span></a>, <a class="txt" href="#E6:74"><span class="lab"><font color="Green" title="E67">A6</font></span></a>, <a class="txt" href="#E7:74"><span class="lab"><font color="Green" title="E68">A7</font></span></a>, <a class="ref" href="jgraph_6.html#T58" target="_self" title="JGRAPH_6:th.58">Th58</a></span>;<br/>
<a NAME="E12:74"/><span class="lab"><font color="Green" title="E72">A11</font></span>: 
<span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></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> <span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></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"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="ref" href="jgraph_6.html#T44" target="_self" title="JGRAPH_6:th.44">Th44</a></span>;<br/>
<a NAME="E13:74"/>
<span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">c</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></span>;<br/>
<a NAME="E14:74"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A12</font></span>: 
( <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> or <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <span class="p1"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="ref" href="euclid.html#T56" title="EUCLID:th.56">EUCLID:56</a></span>;<br/>
<a NAME="E15:74"/><span class="lab"><font color="Green" title="E74">A13</font></span>: 
<font color="Maroon" title="c2">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></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> <span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="txt" href="#E5:74"><span class="lab"><font color="Green" title="E66">A5</font></span></a>, <a class="txt" href="#E6:74"><span class="lab"><font color="Green" title="E67">A6</font></span></a>, <a class="txt" href="#E8:74"><span class="lab"><font color="Green" title="E69">A8</font></span></a>, <a class="ref" href="jgraph_6.html#T58" target="_self" title="JGRAPH_6:th.58">Th58</a></span>;<br/>
<a NAME="E16:74"/>
<span class="p1">(<span class="default"><a href="rltopsp1.html#K1" title="RLTOPSP1:func.1">LSeg</a> <span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></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> <span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span>,<span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c6">d</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></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"><span class="p2"><a href="euclid.html#K19" title="EUCLID:func.19">|[</a><span class="default"><font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font></span><a href="euclid.html#K19" title="EUCLID:func.19">]|</a></span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="ref" href="jgraph_6.html#T42" target="_self" title="JGRAPH_6:th.42">Th42</a></span>;<br/>
<span class="kw">hence </span><a NAME="E17:74"/>
( <font color="Maroon" title="c1">P1</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c10">p2</font> &amp; <font color="Maroon" title="c2">P2</font> <a href="topreal1.html#R1" title="TOPREAL1:pred.1">is_an_arc_of</a> <font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c10">p2</font> &amp; not <font color="Maroon" title="c1">P1</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; not <font color="Maroon" title="c2">P2</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp;  <a href="jgraph_6.html#NK1" title="JGRAPH_6:NK.1">rectangle</a> <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>,<font color="Maroon" title="c5">c</font>,<font color="Maroon" title="c6">d</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">P1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c2">P2</font> &amp; <font color="Maroon" title="c1">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c2">P2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K2" title="TARSKI:func.2">{</a><span class="default"><font color="Maroon" title="c9">p1</font>,<font color="Maroon" title="c10">p2</font></span><a href="tarski.html#K2" title="TARSKI:func.2">}</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:74"><span class="lab"><font color="Green" title="E62">A1</font></span></a>, <a class="txt" href="#E2:74"><span class="lab"><font color="Green" title="E63">A2</font></span></a>, <a class="txt" href="#E3:74"><span class="lab"><font color="Green" title="E64">A3</font></span></a>, <a class="txt" href="#E4:74"><span class="lab"><font color="Green" title="E65">A4</font></span></a>, <a class="txt" href="#E5:74"><span class="lab"><font color="Green" title="E66">A5</font></span></a>, <a class="txt" href="#E6:74"><span class="lab"><font color="Green" title="E67">A6</font></span></a>, <a class="txt" href="#E7:74"><span class="lab"><font color="Green" title="E68">A7</font></span></a>, <a class="txt" href="#E8:74"><span class="lab"><font color="Green" title="E69">A8</font></span></a>, <a class="txt" href="#E10:74"><span class="lab"><font color="Green" title="E70">A9</font></span></a>, <a class="txt" href="#E11:74"><span class="lab"><font color="Green" title="E71">A10</font></span></a>, <a class="txt" href="#E12:74"><span class="lab"><font color="Green" title="E72">A11</font></span></a>, <a class="txt" href="#E14:74"><span class="lab"><font color="Green" title="E73">A12</font></span></a>, <a class="txt" href="#E15:74"><span class="lab"><font color="Green" title="E74">A13</font></span></a>, <a class="ref" href="jgraph_6.html#T58" target="_self" title="JGRAPH_6:th.58">Th58</a>, <a class="ref" href="topreal1.html#T18" title="TOPREAL1:th.18">TOPREAL1:18</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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