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<b>let </b><font color="Maroon" title="c8">S</font> be  <a href="toprealb.html#V1" title="TOPREALB:attr.1">being_simple_closed_curve</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of  <a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2; <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#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c8">S</font> holds   <a href="gr_cy_1.html#K2" title="GR_CY_1:func.2">INT.Group</a> , <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c8">S</font>,<font color="Olive" title="b1">x</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/><b>let </b><font color="Maroon" title="c9">x</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c8">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="gr_cy_1.html#K2" title="GR_CY_1:func.2">INT.Group</a> , <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c8">S</font>,<font color="Maroon" title="c9">x</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> </span><br/>



<b>consider </b><font color="Maroon" title="c10">r</font> being  <a href="xxreal_0.html#V2" title="XXREAL_0:attr.2">positive</a> <a href="xreal_0.html#V1" title="XREAL_0:attr.1">real</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a> , <font color="Maroon" title="c11">o</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>, <font color="Maroon" title="c12">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c10">r</font></span>)</span>;<br/>
<a NAME="E2:45"/><i><font color="Green" title="E43">A1</font></i>: 
 <a href="gr_cy_1.html#K2" title="GR_CY_1:func.2">INT.Group</a> , <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c10">r</font></span>)</span>,<font color="Maroon" title="c12">y</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> 
 
<b>by </b><i><a class="txt" href="topalg_5.html#E48"><i><font color="Green" title="E41">Lm16</font></i></a></i>;<br/>
<a NAME="E3:45"/>
 <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <span class="p1">(<span class="default"><a href="toprealb.html#K7" title="TOPREALB:func.7">Tcircle</a> <font color="Maroon" title="c11">o</font>,<font color="Maroon" title="c10">r</font></span>)</span>,<font color="Maroon" title="c12">y</font>, <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c8">S</font>,<font color="Maroon" title="c9">x</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> 
 
<b>by </b><i><a class="ref" href="topalg_3.html#T35" title="TOPALG_3:th.35">TOPALG_3:35</a>, <a class="ref" href="toprealb.html#T11" title="TOPREALB:th.11">TOPREALB:11</a></i>;<br/>
<b>hence </b><a NAME="E4:45"/>
 <a href="gr_cy_1.html#K2" title="GR_CY_1:func.2">INT.Group</a> , <a href="topalg_1.html#NK4" title="TOPALG_1:NK.4">pi_1</a> <font color="Maroon" title="c8">S</font>,<font color="Maroon" title="c9">x</font> <a href="group_6.html#R2" title="GROUP_6:pred.2">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="#E2:45"><i><font color="Green" title="E43">A1</font></i></a>, <a class="ref" href="group_6.html#T78" title="GROUP_6:th.78">GROUP_6:78</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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