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<b>consider </b><font color="Maroon" title="c2">T</font> being   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/>
<b>take </b>
<font color="Maroon" title="c1">I</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <font color="Maroon" title="c2">T</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">I</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <font color="Maroon" title="c2">T</font> is <a href="waybel18.html#V1" title="WAYBEL18:attr.1">TopSpace-yielding</a></span><br/>

<b>let </b><font color="Maroon" title="c3">v</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel18.html#D1" target="_self" title="WAYBEL18:def.1">WAYBEL18:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <font color="Maroon" title="c2">T</font></span>)</span> implies <font color="Maroon" title="c3">v</font> is    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a>  )</span><br/>

<a NAME="E2:5_1_1"/><i><font color="Green" title="E4">A1</font></i>: 
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <font color="Maroon" title="c2">T</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><font color="Maroon" title="c2">T</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="funcop_1.html#T19" title="FUNCOP_1:th.19">FUNCOP_1:19</a></i>;<br/>
<b>assume </b><a NAME="E3:5_1_1"/>
<font color="Maroon" title="c3">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">I</font> <a href="pre_circ.html#K1" title="PRE_CIRC:func.1">--&gt;</a> <font color="Maroon" title="c2">T</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">v</font> is    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> </span><br/>

<b>hence </b><a NAME="E4:5_1_1"/>
<font color="Maroon" title="c3">v</font> is    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> 
 <b>by </b><i><a class="txt" href="#E2:5_1_1"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</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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