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<span class="kw">let </span><font color="Maroon" title="c1">T</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" 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">  for <font color="Olive" title="b1">t</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b2">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b3">s</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b2">S</font><br/>  for <font color="Olive" title="b4">f</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Olive" title="b1">t</font><br/>  for <font color="Olive" title="b5">g</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Olive" title="b3">s</font>  st <font color="Olive" title="b1">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">s</font> &amp; <font color="Olive" title="b4">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b5">g</font> &amp; <font color="Olive" title="b5">g</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a>  holds <br/><font color="Olive" title="b4">f</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">t</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">  for <font color="Olive" title="b1">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">T</font><br/>  for <font color="Olive" title="b2">s</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Olive" title="b1">S</font><br/>  for <font color="Olive" title="b3">f</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c2">t</font><br/>  for <font color="Olive" title="b4">g</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Olive" title="b2">s</font>  st <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">s</font> &amp; <font color="Olive" title="b3">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b4">g</font> &amp; <font color="Olive" title="b4">g</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a>  holds <br/><font color="Olive" title="b3">f</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">S</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</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">  for <font color="Olive" title="b1">s</font> being   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c3">S</font><br/>  for <font color="Olive" title="b2">f</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c2">t</font><br/>  for <font color="Olive" title="b3">g</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Olive" title="b1">s</font>  st <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">s</font> &amp; <font color="Olive" title="b2">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b3">g</font> &amp; <font color="Olive" title="b3">g</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a>  holds <br/><font color="Olive" title="b2">f</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">s</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c3">S</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">  for <font color="Olive" title="b1">f</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c2">t</font><br/>  for <font color="Olive" title="b2">g</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c4">s</font>  st <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> &amp; <font color="Olive" title="b1">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b2">g</font> &amp; <font color="Olive" title="b2">g</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a>  holds <br/><font color="Olive" title="b1">f</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c5">f</font> be   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c2">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">  for <font color="Olive" title="b1">g</font> being   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c4">s</font>  st <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> &amp; <font color="Maroon" title="c5">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Olive" title="b1">g</font> &amp; <font color="Olive" title="b1">g</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a>  holds <br/><font color="Maroon" title="c5">f</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c6">g</font> be   <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c4">s</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"> ( <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> &amp; <font color="Maroon" title="c5">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">g</font> &amp; <font color="Maroon" title="c6">g</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a>  implies <font color="Maroon" title="c5">f</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a>  )</span><br/>











<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:32"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
( <font color="Maroon" title="c2">t</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">s</font> &amp; <font color="Maroon" title="c5">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c6">g</font> )
 <span class="kw">and </span><br/><a NAME="E2:32"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
<font color="Maroon" title="c6">g</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</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"> <font color="Maroon" title="c5">f</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</a> </span><br/>

<span class="kw">consider </span><font color="Maroon" title="c7">c</font> being   <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c4">s</font><span class="kw"> such that </span><br/><a NAME="E4:32"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
<font color="Maroon" title="c6">g</font>,<font color="Maroon" title="c7">c</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:32"><span class="lab"><font color="Green" title="E20">A2</font></span></a></span>;<br/>
<font color="Maroon" title="c7">c</font> = 
<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <a href="struct_0.html#K6" title="STRUCT_0:func.6">--&gt;</a> <font color="Maroon" title="c4">s</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="borsuk_2.html#T5" onmouseover="rs('borsuk_2/T5')" onmouseout="rh()">BORSUK_2:5</a></span>
<br/>.= 
<a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> <a href="struct_0.html#K6" title="STRUCT_0:func.6">--&gt;</a> <font color="Maroon" title="c2">t</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E19">A1</font></span></a></span>
;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c8">c</font> = <font color="Maroon" title="c7">c</font> as   <a href="funct_1.html#V3" title="FUNCT_1:attr.3">constant</a>  <a href="topalg_1.html#NM1" title="TOPALG_1:NM.1">Loop</a> of <font color="Maroon" title="c2">t</font> <span class="kw">by</span> <span class="lab"><a class="ref" href="jordan.html#T41" onmouseover="rs('jordan/T41')" onmouseout="rh()">JORDAN:41</a></span>;<br/>
<a NAME="E7:32"/>
<font color="Maroon" title="c5">f</font>,<font color="Maroon" title="c8">c</font> <a href="borsuk_2.html#R3" title="BORSUK_2:pred.3">are_homotopic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:32"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="txt" href="#E4:32"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="ref" href="topalg_6.html#T6" target="_self" onmouseover="rs('topalg_6/T6')" onmouseout="rh()">Th6</a></span>;<br/>
<span class="kw">hence </span><a NAME="E8:32"/>
<font color="Maroon" title="c5">f</font> is  <a href="topalg_6.html#V3" title="TOPALG_6:attr.3">nullhomotopic</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"> verum</span><br/>


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