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<span class="kw">let </span><font color="Maroon" title="c4">a</font>, <font color="Maroon" title="c5">b</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font>; <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"> ( <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">R62</a>(<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>) implies <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">R62</a>(<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">a</font>) )</span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">P</font> =  the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>;<br/>
<span class="kw">assume </span><a NAME="E1:49_1_2"/><span class="lab"><font color="Green" title="E39">A1</font></span>: 
<font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> <a href="borsuk_2.html#R2" title="BORSUK_2:pred.2">are_connected</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"> <a href="borsuk_2.html#R1" title="BORSUK_2:pred.1">R62</a>(<font color="Maroon" title="c1">T</font>,<font color="Maroon" title="c5">b</font>,<font color="Maroon" title="c4">a</font>)</span><br/>

<a NAME="E2:49_1_2"/><span class="kw">then </span><span class="lab"><font color="Green" title="E40">A2</font></span>: 
 the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_2.html#D2" onmouseover="rs('borsuk_2/D2')" onmouseout="rh()">BORSUK_2:def 2</a></span>;<br/>
<span class="kw">take </span>
 <a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a>  the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font>
; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="borsuk_2.html#D1" onmouseover="rs('borsuk_2/D1')" onmouseout="rh()">BORSUK_2:def 1</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"> (  <a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a>  the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp; <span class="p1">(<span class="default"><a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a>  the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> &amp; <span class="p1">(<span class="default"><a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a>  the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> )</span><br/>

<a NAME="E3:49_1_2"/>
(  the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp;  the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:49_1_2"><span class="lab"><font color="Green" title="E39">A1</font></span></a>, <a class="ref" href="borsuk_2.html#D2" onmouseover="rs('borsuk_2/D2')" onmouseout="rh()">BORSUK_2:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:49_1_2"/>
(  <a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a>  the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font> is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp; <span class="p1">(<span class="default"><a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a>  the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">b</font> &amp; <span class="p1">(<span class="default"><a href="borsuk_2.html#K2" title="BORSUK_2:func.2">-</a>  the    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c4">a</font>,<font color="Maroon" title="c5">b</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">a</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:49_1_2"><span class="lab"><font color="Green" title="E40">A2</font></span></a>, <a class="ref" href="borsuk_6.html#T41" target="_self" onmouseover="rs('borsuk_6/T41')" onmouseout="rh()">Th41</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/>


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