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<b>let </b><font color="Maroon" title="c1">GX</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <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>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">GX</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="connsp_1.html#R2" title="CONNSP_1:pred.2">are_joined</a>  ) implies <font color="Maroon" title="c1">GX</font> is <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a> )</span><br/>

<b>assume </b><a NAME="E1:35"/>
for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">GX</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="connsp_1.html#R2" title="CONNSP_1:pred.2">are_joined</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">GX</font> is <a href="connsp_1.html#V1" title="CONNSP_1:attr.1">connected</a></span><br/>

<a NAME="E2:35"/><b>then </b>
 ex <font color="Olive" title="b1">x</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">GX</font> st <br/>for <font color="Olive" title="b2">y</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">GX</font> holds  <font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font> <a href="connsp_1.html#R2" title="CONNSP_1:pred.2">are_joined</a> 
 
<b>by </b><i><a class="ref" href="connsp_1.html#T31" target="_self" title="CONNSP_1:th.31">Th31</a></i>;<br/>
<b>hence </b><a NAME="E3:35"/>
<font color="Maroon" title="c1">GX</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#T30" target="_self" title="CONNSP_1:th.30">Th30</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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