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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">D</font> being non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font><br/> for <font color="Olive" title="b2">W</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K12" title="BORSUK_1:func.12">space</a> <font color="Olive" title="b1">D</font></span>)</span>  ex <font color="Olive" title="b3">W9</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> st <span class="p1">(<span class="default"><a href="borsuk_1.html#K13" title="BORSUK_1:func.13">Proj</a> <font color="Olive" title="b1">D</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">W9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">W</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">D</font> be  non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">W</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K12" title="BORSUK_1:func.12">space</a> <font color="Maroon" title="c2">D</font></span>)</span>  ex <font color="Olive" title="b2">W9</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> st <span class="p1">(<span class="default"><a href="borsuk_1.html#K13" title="BORSUK_1:func.13">Proj</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">W9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">W</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">W</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="borsuk_1.html#K12" title="BORSUK_1:func.12">space</a> <font color="Maroon" title="c2">D</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">W9</font> being  <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font> st <span class="p1">(<span class="default"><a href="borsuk_1.html#K13" title="BORSUK_1:func.13">Proj</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">W9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W</font></span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c4">p</font> = <font color="Maroon" title="c3">W</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of <font color="Maroon" title="c2">D</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#D10" target="_self" title="BORSUK_1:def.10">Def10</a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c5">W9</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">X</font><span class="kw"> such that </span><br/><a NAME="E3:87"/><span class="lab"><font color="Green" title="E55">A1</font></span>: 
<span class="p1">(<span class="default"><a href="borsuk_1.html#K1" title="BORSUK_1:func.1">proj</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">W9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">p</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_1.html#T32" target="_self" title="BORSUK_1:th.32">Th32</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c5">W9</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="borsuk_1.html#K13" title="BORSUK_1:func.13">Proj</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">W9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W</font></span><br/>

<span class="kw">thus </span><a NAME="E4:87"/>
<span class="p1">(<span class="default"><a href="borsuk_1.html#K13" title="BORSUK_1:func.13">Proj</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">W9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">W</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:87"><span class="lab"><font color="Green" title="E55">A1</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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