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<b>let </b><font color="Maroon" title="c2">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="topalg_2.html#V3" title="TOPALG_2:attr.3">convex</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of  <a href="topalg_2.html#K3" title="TOPALG_2:func.3">R^1</a> ;<br/><b>let </b><font color="Maroon" title="c3">a</font>, <font color="Maroon" title="c4">b</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">T</font>;<br/><b>let </b><font color="Maroon" title="c5">P</font>, <font color="Maroon" title="c6">Q</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c3">a</font>,<font color="Maroon" title="c4">b</font>;<br/>





<b>set </b><font color="Maroon" title="c7">F</font> =  <a href="topalg_2.html#K4" title="TOPALG_2:func.4">R1Homotopy</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">Q</font>;<br/>
<b>let </b><font color="Maroon" title="c8">s</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="topalg_2.html#K4" title="TOPALG_2:func.4">R1Homotopy</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">Q</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c8">s</font>,0 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 0</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">0 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">Q</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topalg_2.html#D5" target="_self" title="TOPALG_2:def.5">Def5</a>, <a class="ref" href="borsuk_1.html#D17" title="BORSUK_1:def.17">BORSUK_1:def 17</a></i>
<br/>.= 
<font color="Maroon" title="c5">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font>

;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="topalg_2.html#K4" title="TOPALG_2:func.4">R1Homotopy</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">Q</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c8">s</font>,1 = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="real_1.html#K5" title="REAL_1:func.5">-</a> 1</span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default">1 <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">Q</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topalg_2.html#D5" target="_self" title="TOPALG_2:def.5">Def5</a>, <a class="ref" href="borsuk_1.html#D18" title="BORSUK_1:def.18">BORSUK_1:def 18</a></i>
<br/>.= 
<font color="Maroon" title="c6">Q</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font>

;<br/>

<b>let </b><font color="Maroon" title="c9">t</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <a href="topmetr.html#K5" title="TOPMETR:func.5">I[01]</a> ;<br/>

<a NAME="E3:35"/><i><font color="Green" title="E25">A1</font></i>: 
<font color="Maroon" title="c5">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="borsuk_1.html#K21" title="BORSUK_1:func.21">0[01]</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D17" title="BORSUK_1:def.17">BORSUK_1:def 17</a>, <a class="ref" href="borsuk_2.html#D4" title="BORSUK_2:def.4">BORSUK_2:def 4</a></i>;<br/>
<a NAME="E4:35"/><i><font color="Green" title="E26">A2</font></i>: 
<font color="Maroon" title="c6">Q</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="borsuk_1.html#K21" title="BORSUK_1:func.21">0[01]</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">a</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D17" title="BORSUK_1:def.17">BORSUK_1:def 17</a>, <a class="ref" href="borsuk_2.html#D4" title="BORSUK_2:def.4">BORSUK_2:def 4</a></i>;<br/>
<a NAME="E5:35"/><i><font color="Green" title="E27">A3</font></i>: 
<font color="Maroon" title="c5">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="borsuk_1.html#K22" title="BORSUK_1:func.22">1[01]</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D18" title="BORSUK_1:def.18">BORSUK_1:def 18</a>, <a class="ref" href="borsuk_2.html#D4" title="BORSUK_2:def.4">BORSUK_2:def 4</a></i>;<br/>
<a NAME="E6:35"/><i><font color="Green" title="E28">A4</font></i>: 
<font color="Maroon" title="c6">Q</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="borsuk_1.html#K22" title="BORSUK_1:func.22">1[01]</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">b</font>
 
<b>by </b><i><a class="ref" href="borsuk_1.html#D18" title="BORSUK_1:def.18">BORSUK_1:def 18</a>, <a class="ref" href="borsuk_2.html#D4" title="BORSUK_2:def.4">BORSUK_2:def 4</a></i>;<br/>
<b>thus </b><span class="p1">(<span class="default"><a href="topalg_2.html#K4" title="TOPALG_2:func.4">R1Homotopy</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">Q</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> 0,<font color="Maroon" title="c9">t</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">t</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="borsuk_1.html#K21" title="BORSUK_1:func.21">0[01]</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">Q</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="borsuk_1.html#K21" title="BORSUK_1:func.21">0[01]</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topalg_2.html#D5" target="_self" title="TOPALG_2:def.5">Def5</a>, <a class="ref" href="borsuk_1.html#D17" title="BORSUK_1:def.17">BORSUK_1:def 17</a></i>
<br/>.= 
<font color="Maroon" title="c3">a</font>
<b>by </b><i><a class="txt" href="topalg_2.html#E3:35"><i><font color="Green" title="E25">A1</font></i></a>, <a class="txt" href="topalg_2.html#E4:35"><i><font color="Green" title="E26">A2</font></i></a></i>
;<br/>

<b>thus </b><span class="p1">(<span class="default"><a href="topalg_2.html#K4" title="TOPALG_2:func.4">R1Homotopy</a> <font color="Maroon" title="c5">P</font>,<font color="Maroon" title="c6">Q</font></span>)</span> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> 1,<font color="Maroon" title="c9">t</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">1 <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c9">t</font></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">P</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="borsuk_1.html#K22" title="BORSUK_1:func.22">1[01]</a> </span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">t</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c6">Q</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <a href="borsuk_1.html#K22" title="BORSUK_1:func.22">1[01]</a> </span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="topalg_2.html#D5" target="_self" title="TOPALG_2:def.5">Def5</a>, <a class="ref" href="borsuk_1.html#D18" title="BORSUK_1:def.18">BORSUK_1:def 18</a></i>
<br/>.= 
<font color="Maroon" title="c4">b</font>
<b>by </b><i><a class="txt" href="topalg_2.html#E5:35"><i><font color="Green" title="E27">A3</font></i></a>, <a class="txt" href="topalg_2.html#E6:35"><i><font color="Green" title="E28">A4</font></i></a></i>
;<br/>


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