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<span class="kw">let </span><font color="Maroon" title="c1">n</font> be   <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</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">p</font>, <font color="Olive" title="b2">q</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> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span></span>)</span>  st <font color="Olive" title="b1">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span></span>)</span> holds <br/> <a href="mfold_2.html#K3" title="MFOLD_2:func.3">TPlane</a> (<font color="Olive" title="b1">p</font>,<font color="Olive" title="b2">q</font>) is <font color="Maroon" title="c1">n</font> <a href="mfold_1.html#V3" title="MFOLD_1:attr.3">-manifold</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font>, <font color="Maroon" title="c3">q</font> be   <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> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span></span>)</span> implies  <a href="mfold_2.html#K3" title="MFOLD_2:func.3">TPlane</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>) is <font color="Maroon" title="c1">n</font> <a href="mfold_1.html#V3" title="MFOLD_1:attr.3">-manifold</a>  )</span><br/>



<span class="kw">assume </span><a NAME="E1:39"/>
<font color="Maroon" title="c2">p</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">n</font> <a href="binop_2.html#K23" title="BINOP_2:func.23">+</a> 1</span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="mfold_2.html#K3" title="MFOLD_2:func.3">TPlane</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>) is <font color="Maroon" title="c1">n</font> <a href="mfold_1.html#V3" title="MFOLD_1:attr.3">-manifold</a> </span><br/>

<a NAME="E2:39"/><span class="kw">then </span>
 <a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> <font color="Maroon" title="c1">n</font>, <a href="mfold_2.html#K3" title="MFOLD_2:func.3">TPlane</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>) <a href="mfold_2.html#R1" title="MFOLD_2:pred.1">are_homeomorphic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="mfold_2.html#T29" target="_self" title="MFOLD_2:th.29">Th29</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:39"/>
 <a href="mfold_2.html#K3" title="MFOLD_2:func.3">TPlane</a> (<font color="Maroon" title="c2">p</font>,<font color="Maroon" title="c3">q</font>) is <font color="Maroon" title="c1">n</font> <a href="mfold_1.html#V3" title="MFOLD_1:attr.3">-manifold</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mfold_2.html#T12" target="_self" title="MFOLD_2:th.12">Th12</a></span>; <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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