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<span class="kw">let </span><font color="Maroon" title="c1">Y</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">y</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font>  st  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Olive" title="b1">y</font> is  <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>  holds <br/> not <font color="Maroon" title="c1">Y</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">y</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">Y</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</font> is  <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>  implies  not <font color="Maroon" title="c1">Y</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:33"/>
 <a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</font> is  <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  not <font color="Maroon" title="c1">Y</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> </span><br/>

<a NAME="E2:33"/><span class="kw">then </span>
 not <font color="Maroon" title="c1">Y</font> is 1 <a href="struct_0.html#V13" title="STRUCT_0:attr.13">-element</a> 
 
;<br/>
<a NAME="E3:33"/><span class="kw">then </span>
 not  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">Y</font> is 1 <a href="card_1.html#V3" title="CARD_1:attr.3">-element</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="struct_0.html#D19" title="STRUCT_0:def.19">STRUCT_0:def 19</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:33"/>
 not <font color="Maroon" title="c1">Y</font> is  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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