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<b>let </b><font color="Maroon" title="c1">Y</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ;<br/><b>let </b><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>;<br/>



<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:45_1"/><i><font color="Green" title="E15">A1</font></i>: 
 <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#V2" title="TEX_2:attr.2">proper</a>
 ;<br/><b>reconsider </b><font color="Maroon" title="c3">A</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</font></span>)</span> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">Y</font> <b>by </b><i><a class="txt" href="tex_2.html#E17"><i><font color="Green" title="E9">Lm1</font></i></a></i>;<br/><a NAME="E3:45_1"/>
<font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>
 <b>by </b><i><a class="ref" href="tex_2.html#D4" target="_self" title="TEX_2:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E4:45_1"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>
 <b>by </b><i><a class="txt" href="tex_2.html#E1:45_1"><i><font color="Green" title="E15">A1</font></i></a>, <a class="ref" href="tex_2.html#D3" target="_self" title="TEX_2:def.3">Def3</a></i>;<br/></div>
<b>end;</b></div>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:45_2"/>
<span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">y</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> is <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>
 ;<br/><a NAME="E2:45_2"/><b>then </b>
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">Y</font>  st <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="tex_2.html#K1" title="TEX_2:func.1">Sspace</a> <font color="Maroon" title="c2">y</font></span>)</span> holds <br/><font color="Olive" title="b1">A</font> is <a href="tex_2.html#V1" title="TEX_2:attr.1">proper</a>
 <b>by </b><i><a class="ref" href="tex_2.html#D4" target="_self" title="TEX_2:def.4">Def4</a></i>;<br/><b>hence </b><a NAME="E3:45_2"/>
 <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#V2" title="TEX_2:attr.2">proper</a>
 <b>by </b><i><a class="ref" href="tex_2.html#D3" target="_self" title="TEX_2:def.3">Def3</a></i>;<br/></div>
<b>end;</b></div>


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