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<span class="kw">let </span><font color="Maroon" title="c1">T1</font>, <font color="Maroon" title="c2">T2</font> be   <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> is  <a href="topdim_1.html#NV6" title="TOPDIM_1:NV.6">finite-ind</a>  implies ( <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> is  <a href="topdim_1.html#NV6" title="TOPDIM_1:NV.6">finite-ind</a>  &amp;  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> ) )</span><br/>



<span class="kw">assume </span><a NAME="E1:52"/><span class="lab"><font color="Green" title="E30">A1</font></span>: 
<span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> is  <a href="topdim_1.html#NV6" title="TOPDIM_1:NV.6">finite-ind</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> is  <a href="topdim_1.html#NV6" title="TOPDIM_1:NV.6">finite-ind</a>  &amp;  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> )</span><br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:52_1"/>
( <font color="Maroon" title="c1">T1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  or <font color="Maroon" title="c2">T2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  or (  not <font color="Maroon" title="c1">T1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Maroon" title="c2">T2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  ) )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_1"><span class="kw">suppose </span></a><a NAME="E1:52_1_1"/><span class="lab"><font color="Green" title="E31">A2</font></span>: 
( <font color="Maroon" title="c1">T1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  or <font color="Maroon" title="c2">T2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> is  <a href="topdim_1.html#NV6" title="TOPDIM_1:NV.6">finite-ind</a>  &amp;  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> )</span><br/><div class="add"><a NAME="E2:52_1_1"/><span class="kw">then </span>
 <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="topdim_1.html#T6" target="_self" onmouseover="rs('topdim_1/T6')" onmouseout="rh()">Th6</a></span>;<br/><span class="kw">hence </span><a NAME="E3:52_1_1"/>
( <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> is  <a href="topdim_1.html#NV6" title="TOPDIM_1:NV.6">finite-ind</a>  &amp;  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52_1_1"><span class="lab"><font color="Green" title="E31">A2</font></span></a>, <a class="ref" href="topdim_1.html#T6" target="_self" onmouseover="rs('topdim_1/T6')" onmouseout="rh()">Th6</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="52_1_2"><span class="kw">suppose </span></a><a NAME="E1:52_1_2"/>
(  not <font color="Maroon" title="c1">T1</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp;  not <font color="Maroon" title="c2">T2</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  )
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> is  <a href="topdim_1.html#NV6" title="TOPDIM_1:NV.6">finite-ind</a>  &amp;  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> )</span><br/><div class="add"><a NAME="E2:52_1_2"/><span class="kw">then </span>
<span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="borsuk_3.html#R1" title="BORSUK_3:pred.1">are_homeomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow12.html#T44" onmouseover="rs('yellow12/T44')" onmouseout="rh()">YELLOW12:44</a></span>;<br/><span class="kw">hence </span><a NAME="E3:52_1_2"/>
( <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> is  <a href="topdim_1.html#NV6" title="TOPDIM_1:NV.6">finite-ind</a>  &amp;  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c1">T1</font>,<font color="Maroon" title="c2">T2</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="topdim_1.html#K4" title="TOPDIM_1:func.4">ind</a> <span class="p1"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">[:</a><span class="default"><font color="Maroon" title="c2">T2</font>,<font color="Maroon" title="c1">T1</font></span><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">:]</a></span> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:52"><span class="lab"><font color="Green" title="E30">A1</font></span></a>, <a class="txt" href="topdim_1.html#E38"><span class="lab"><font color="Green" title="E28">Lm9</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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