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<b>let </b><font color="Maroon" title="c1">GX</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">X'</font> being   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">GX</font><br/> for <font color="Olive" title="b2">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font><br/> for <font color="Olive" title="b3">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">X'</font>  st <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">B</font> holds <br/>( <font color="Olive" title="b2">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> iff <font color="Olive" title="b3">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> )</span><br/><b>let </b><font color="Maroon" title="c2">X'</font> be    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">GX</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font><br/> for <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X'</font>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">B</font> holds <br/>( <font color="Olive" title="b1">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> iff <font color="Olive" title="b2">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> )</span><br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X'</font>  st <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">B</font> holds <br/>( <font color="Maroon" title="c3">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> iff <font color="Olive" title="b1">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> )</span><br/><b>let </b><font color="Maroon" title="c4">B</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X'</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> implies ( <font color="Maroon" title="c3">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> iff <font color="Maroon" title="c4">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> ) )</span><br/>







<b>assume </b><a NAME="E1:26"/><i><font color="Green" title="E22">A1</font></i>: 
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> iff <font color="Maroon" title="c4">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> )</span><br/>

<a NAME="E2:26"/><i><font color="Green" title="E23">A2</font></i>: 
(  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">A</font> &amp;  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">B</font> )
 
<b>by </b><i><a class="ref" href="pre_topc.html#D10" title="PRE_TOPC:def.10">PRE_TOPC:def 10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">GX'</font> = <font color="Maroon" title="c1">GX</font>, <font color="Maroon" title="c6">X</font> = <font color="Maroon" title="c2">X'</font> as   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a> ;<br/>
<b>reconsider </b><font color="Maroon" title="c7">A'</font> = <font color="Maroon" title="c3">A</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c5">GX'</font> ;<br/>
<b>reconsider </b><font color="Maroon" title="c8">B'</font> = <font color="Maroon" title="c4">B</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c6">X</font> ;<br/>
<a NAME="E6:26"/><i><font color="Green" title="E24">A3</font></i>: 
 <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">B</font></span>)</span>
 
;<br/>
<div><i><font color="Green" title="E25">A4</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:26_1"/>
not <font color="Maroon" title="c3">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c4">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a></span><br/><a NAME="E2:26_1"/><b>then </b>
not <font color="Maroon" title="c5">GX'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c7">A'</font> is <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a>
 <b>by </b><i><a class="ref" href="connsp_1.html#D3" target="_self" title="CONNSP_1:def.3">Def3</a></i>;<br/><b>then consider </b><font color="Maroon" title="c9">P</font>, <font color="Maroon" title="c10">Q</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">A</font></span>)</span><b> such that </b><br/><a NAME="E4:26_1"/><i><font color="Green" title="E26">A5</font></i>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">P</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c10">Q</font>
 <b>and </b><br/><a NAME="E5:26_1"/><i><font color="Green" title="E27">A6</font></i>: 
<font color="Maroon" title="c9">P</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">A</font></span>)</span>
 <b>and </b><br/><a NAME="E6:26_1"/><i><font color="Green" title="E28">A7</font></i>: 
<font color="Maroon" title="c10">Q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">A</font></span>)</span>
 <b>and </b><br/><a NAME="E7:26_1"/><i><font color="Green" title="E29">A8</font></i>: 
<font color="Maroon" title="c9">P</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>and </b><br/><a NAME="E8:26_1"/><i><font color="Green" title="E30">A9</font></i>: 
<font color="Maroon" title="c10">Q</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>and </b><br/><a NAME="E9:26_1"/><i><font color="Green" title="E31">A10</font></i>: 
<font color="Maroon" title="c9">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c10">Q</font>
 <b>by </b><i><a class="ref" href="connsp_1.html#T11" target="_self" title="CONNSP_1:th.11">Th11</a></i>;<br/><b>consider </b><font color="Maroon" title="c11">P1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font><b> such that </b><br/><a NAME="E11:26_1"/><i><font color="Green" title="E32">A11</font></i>: 
<font color="Maroon" title="c11">P1</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>and </b><br/><a NAME="E12:26_1"/><i><font color="Green" title="E33">A12</font></i>: 
<font color="Maroon" title="c11">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">P</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E7:26_1"><i><font color="Green" title="E29">A8</font></i></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></i>;<br/><b>consider </b><font color="Maroon" title="c12">Q1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font><b> such that </b><br/><a NAME="E14:26_1"/><i><font color="Green" title="E34">A13</font></i>: 
<font color="Maroon" title="c12">Q1</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>and </b><br/><a NAME="E15:26_1"/><i><font color="Green" title="E35">A14</font></i>: 
<font color="Maroon" title="c12">Q1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Q</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E8:26_1"><i><font color="Green" title="E30">A9</font></i></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">PP</font> = <font color="Maroon" title="c9">P</font>, <font color="Maroon" title="c14">QQ</font> = <font color="Maroon" title="c10">Q</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">X'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">B</font></span>)</span> <b>by </b><i><a class="txt" href="connsp_1.html#E1:26"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c15">P11</font> = <font color="Maroon" title="c11">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X'</font> ;<br/><a NAME="E18:26_1"/><i><font color="Green" title="E36">A15</font></i>: 
<font color="Maroon" title="c15">P11</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>by </b><i><a class="txt" href="connsp_1.html#E11:26_1"><i><font color="Green" title="E32">A11</font></i></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></i>;<br/><a NAME="E19:26_1"/>
( <font color="Maroon" title="c11">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">P1</font> &amp; <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/><a NAME="E20:26_1"/><b>then </b><i><font color="Green" title="E37">A16</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c11">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c9">P</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="connsp_1.html#E12:26_1"><i><font color="Green" title="E33">A12</font></i></a>, <a class="ref" href="xboole_1.html#T27" title="XBOOLE_1:th.27">XBOOLE_1:27</a></i>;<br/><a NAME="E21:26_1"/><i><font color="Green" title="E38">A17</font></i>: 
<font color="Maroon" title="c11">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">P1</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/><a NAME="E22:26_1"/>
<font color="Maroon" title="c9">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E1:26"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E23:26_1"/><b>then </b>
<font color="Maroon" title="c9">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c11">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span>
 <b>by </b><i><a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="connsp_1.html#E12:26_1"><i><font color="Green" title="E33">A12</font></i></a>, <a class="txt" href="connsp_1.html#E21:26_1"><i><font color="Green" title="E38">A17</font></i></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>;<br/><a NAME="E24:26_1"/><b>then </b>
<font color="Maroon" title="c9">P</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>;<br/><a NAME="E25:26_1"/><b>then </b>
<font color="Maroon" title="c15">P11</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">X'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">PP</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E1:26"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="connsp_1.html#E20:26_1"><i><font color="Green" title="E37">A16</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/><a NAME="E26:26_1"/><b>then </b><i><font color="Green" title="E39">A18</font></i>: 
<font color="Maroon" title="c13">PP</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>by </b><i><a class="txt" href="connsp_1.html#E18:26_1"><i><font color="Green" title="E36">A15</font></i></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c16">Q11</font> = <font color="Maroon" title="c12">Q1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X'</font> ;<br/><a NAME="E28:26_1"/><i><font color="Green" title="E40">A19</font></i>: 
<font color="Maroon" title="c16">Q11</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>by </b><i><a class="txt" href="connsp_1.html#E14:26_1"><i><font color="Green" title="E34">A13</font></i></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></i>;<br/><a NAME="E29:26_1"/>
( <font color="Maroon" title="c12">Q1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Q1</font> &amp; <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c3">A</font> )
 <b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/><a NAME="E30:26_1"/><b>then </b><i><font color="Green" title="E41">A20</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c12">Q1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c10">Q</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="connsp_1.html#E15:26_1"><i><font color="Green" title="E35">A14</font></i></a>, <a class="ref" href="xboole_1.html#T27" title="XBOOLE_1:th.27">XBOOLE_1:27</a></i>;<br/><a NAME="E31:26_1"/><i><font color="Green" title="E42">A21</font></i>: 
<font color="Maroon" title="c12">Q1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">A</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Q1</font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></i>;<br/><a NAME="E32:26_1"/>
<font color="Maroon" title="c10">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E1:26"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="xboole_1.html#T1" title="XBOOLE_1:th.1">XBOOLE_1:1</a></i>;<br/><a NAME="E33:26_1"/><b>then </b>
<font color="Maroon" title="c10">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c12">Q1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span>
 <b>by </b><i><a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="connsp_1.html#E15:26_1"><i><font color="Green" title="E35">A14</font></i></a>, <a class="txt" href="connsp_1.html#E31:26_1"><i><font color="Green" title="E42">A21</font></i></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>;<br/><a NAME="E34:26_1"/><b>then </b>
<font color="Maroon" title="c10">Q</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">Q1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">A</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="xboole_1.html#T19" title="XBOOLE_1:th.19">XBOOLE_1:19</a></i>;<br/><a NAME="E35:26_1"/><b>then </b>
<span class="p1">(<span class="default"><font color="Maroon" title="c12">Q1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Q</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E30:26_1"><i><font color="Green" title="E41">A20</font></i></a>, <a class="ref" href="xboole_0.html#D10" title="XBOOLE_0:def.10">XBOOLE_0:def 10</a></i>;<br/><a NAME="E36:26_1"/><b>then </b>
<font color="Maroon" title="c14">QQ</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>by </b><i><a class="txt" href="connsp_1.html#E1:26"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="connsp_1.html#E28:26_1"><i><font color="Green" title="E40">A19</font></i></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></i>;<br/><a NAME="E37:26_1"/><b>then </b>
not <font color="Maroon" title="c6">X</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c8">B'</font> is <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a>
 <b>by </b><i><a class="txt" href="connsp_1.html#E1:26"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="connsp_1.html#E6:26"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="connsp_1.html#E4:26_1"><i><font color="Green" title="E26">A5</font></i></a>, <a class="txt" href="connsp_1.html#E5:26_1"><i><font color="Green" title="E27">A6</font></i></a>, <a class="txt" href="connsp_1.html#E6:26_1"><i><font color="Green" title="E28">A7</font></i></a>, <a class="txt" href="connsp_1.html#E9:26_1"><i><font color="Green" title="E31">A10</font></i></a>, <a class="txt" href="connsp_1.html#E26:26_1"><i><font color="Green" title="E39">A18</font></i></a>, <a class="ref" href="connsp_1.html#T11" target="_self" title="CONNSP_1:th.11">Th11</a></i>;<br/><b>hence </b><a NAME="E38:26_1"/>
not <font color="Maroon" title="c4">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="connsp_1.html#D3" target="_self" title="CONNSP_1:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:26_2"/>
not <font color="Maroon" title="c4">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> not <font color="Maroon" title="c3">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a></span><br/><a NAME="E2:26_2"/><b>then </b>
not <font color="Maroon" title="c2">X'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">B</font> is <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a>
 <b>by </b><i><a class="ref" href="connsp_1.html#D3" target="_self" title="CONNSP_1:def.3">Def3</a></i>;<br/><b>then consider </b><font color="Maroon" title="c9">P</font>, <font color="Maroon" title="c10">Q</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">X'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">B</font></span>)</span><b> such that </b><br/><a NAME="E4:26_2"/><i><font color="Green" title="E26">A22</font></i>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">B</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">P</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <font color="Maroon" title="c10">Q</font>
 <b>and </b><br/><a NAME="E5:26_2"/><i><font color="Green" title="E27">A23</font></i>: 
<font color="Maroon" title="c9">P</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">B</font></span>)</span>
 <b>and </b><br/><a NAME="E6:26_2"/><i><font color="Green" title="E28">A24</font></i>: 
<font color="Maroon" title="c10">Q</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K1" title="STRUCT_0:func.1">{}</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">X'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">B</font></span>)</span>
 <b>and </b><br/><a NAME="E7:26_2"/><i><font color="Green" title="E29">A25</font></i>: 
<font color="Maroon" title="c9">P</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>and </b><br/><a NAME="E8:26_2"/><i><font color="Green" title="E30">A26</font></i>: 
<font color="Maroon" title="c10">Q</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>and </b><br/><a NAME="E9:26_2"/><i><font color="Green" title="E31">A27</font></i>: 
<font color="Maroon" title="c9">P</font> <a href="xboole_0.html#R1" title="XBOOLE_0:pred.1">misses</a> <font color="Maroon" title="c10">Q</font>
 <b>by </b><i><a class="ref" href="connsp_1.html#T11" target="_self" title="CONNSP_1:th.11">Th11</a></i>;<br/><b>consider </b><font color="Maroon" title="c11">P1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X'</font><b> such that </b><br/><a NAME="E11:26_2"/><i><font color="Green" title="E32">A28</font></i>: 
<font color="Maroon" title="c11">P1</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>and </b><br/><a NAME="E12:26_2"/><i><font color="Green" title="E33">A29</font></i>: 
<font color="Maroon" title="c11">P1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">X'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">P</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E7:26_2"><i><font color="Green" title="E29">A25</font></i></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></i>;<br/><b>consider </b><font color="Maroon" title="c12">Q1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">X'</font><b> such that </b><br/><a NAME="E14:26_2"/><i><font color="Green" title="E34">A30</font></i>: 
<font color="Maroon" title="c12">Q1</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>and </b><br/><a NAME="E15:26_2"/><i><font color="Green" title="E35">A31</font></i>: 
<font color="Maroon" title="c12">Q1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">X'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c4">B</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Q</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E8:26_2"><i><font color="Green" title="E30">A26</font></i></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></i>;<br/><b>consider </b><font color="Maroon" title="c13">P2</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font><b> such that </b><br/><a NAME="E17:26_2"/><i><font color="Green" title="E36">A32</font></i>: 
<font color="Maroon" title="c13">P2</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>and </b><br/><a NAME="E18:26_2"/><i><font color="Green" title="E37">A33</font></i>: 
<font color="Maroon" title="c13">P2</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">P1</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E11:26_2"><i><font color="Green" title="E32">A28</font></i></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></i>;<br/><b>consider </b><font color="Maroon" title="c14">Q2</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">GX</font><b> such that </b><br/><a NAME="E20:26_2"/><i><font color="Green" title="E38">A34</font></i>: 
<font color="Maroon" title="c14">Q2</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>and </b><br/><a NAME="E21:26_2"/><i><font color="Green" title="E39">A35</font></i>: 
<font color="Maroon" title="c14">Q2</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">Q1</font>
 <b>by </b><i><a class="txt" href="connsp_1.html#E14:26_2"><i><font color="Green" title="E34">A30</font></i></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c15">PP</font> = <font color="Maroon" title="c9">P</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">A</font></span>)</span> <b>by </b><i><a class="txt" href="connsp_1.html#E1:26"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c16">QQ</font> = <font color="Maroon" title="c10">Q</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">A</font></span>)</span> <b>by </b><i><a class="txt" href="connsp_1.html#E1:26"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a></i>;<br/><font color="Maroon" title="c13">P2</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c13">P2</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">B</font></span>)</span>
<b>by </b><i><a class="txt" href="connsp_1.html#E1:26"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>
<br/>.= 
<font color="Maroon" title="c15">PP</font>
<b>by </b><i><a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="connsp_1.html#E12:26_2"><i><font color="Green" title="E33">A29</font></i></a>, <a class="txt" href="connsp_1.html#E18:26_2"><i><font color="Green" title="E37">A33</font></i></a>, <a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
;<br/><a NAME="E25:26_2"/><b>then </b><i><font color="Green" title="E40">A36</font></i>: 
<font color="Maroon" title="c15">PP</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>by </b><i><a class="txt" href="connsp_1.html#E17:26_2"><i><font color="Green" title="E36">A32</font></i></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></i>;<br/><font color="Maroon" title="c14">Q2</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GX</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c3">A</font></span>)</span></span>)</span> = 
<font color="Maroon" title="c14">Q2</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c2">X'</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <font color="Maroon" title="c4">B</font></span>)</span>
<b>by </b><i><a class="txt" href="connsp_1.html#E1:26"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="ref" href="xboole_1.html#T28" title="XBOOLE_1:th.28">XBOOLE_1:28</a></i>
<br/>.= 
<font color="Maroon" title="c16">QQ</font>
<b>by </b><i><a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="connsp_1.html#E15:26_2"><i><font color="Green" title="E35">A31</font></i></a>, <a class="txt" href="connsp_1.html#E21:26_2"><i><font color="Green" title="E39">A35</font></i></a>, <a class="ref" href="xboole_1.html#T16" title="XBOOLE_1:th.16">XBOOLE_1:16</a></i>
;<br/><a NAME="E27:26_2"/><b>then </b>
<font color="Maroon" title="c16">QQ</font> is <a href="pre_topc.html#V4" title="PRE_TOPC:attr.4">closed</a>
 <b>by </b><i><a class="txt" href="connsp_1.html#E20:26_2"><i><font color="Green" title="E38">A34</font></i></a>, <a class="ref" href="pre_topc.html#T43" title="PRE_TOPC:th.43">PRE_TOPC:43</a></i>;<br/><a NAME="E28:26_2"/><b>then </b>
not <font color="Maroon" title="c5">GX'</font> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c7">A'</font> is <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a>
 <b>by </b><i><a class="txt" href="connsp_1.html#E1:26"><i><font color="Green" title="E22">A1</font></i></a>, <a class="txt" href="connsp_1.html#E2:26"><i><font color="Green" title="E23">A2</font></i></a>, <a class="txt" href="connsp_1.html#E6:26"><i><font color="Green" title="E24">A3</font></i></a>, <a class="txt" href="connsp_1.html#E4:26_2"><i><font color="Green" title="E26">A22</font></i></a>, <a class="txt" href="connsp_1.html#E5:26_2"><i><font color="Green" title="E27">A23</font></i></a>, <a class="txt" href="connsp_1.html#E6:26_2"><i><font color="Green" title="E28">A24</font></i></a>, <a class="txt" href="connsp_1.html#E9:26_2"><i><font color="Green" title="E31">A27</font></i></a>, <a class="txt" href="connsp_1.html#E25:26_2"><i><font color="Green" title="E40">A36</font></i></a>, <a class="ref" href="connsp_1.html#T11" target="_self" title="CONNSP_1:th.11">Th11</a></i>;<br/><b>hence </b><a NAME="E29:26_2"/>
not <font color="Maroon" title="c3">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a>
 <b>by </b><i><a class="ref" href="connsp_1.html#D3" target="_self" title="CONNSP_1:def.3">Def3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E9:26"/>
( <font color="Maroon" title="c3">A</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> iff <font color="Maroon" title="c4">B</font> is <a href="connsp_1.html#V2" title="CONNSP_1:attr.2">connected</a> )
 <b>by </b><i><a class="txt" href="connsp_1.html#E7:26"><i><font color="Green" title="E25">A4</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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